After a goalless draw in the first leg, Real took the lead when Gareth Bale's cross deflected off City's Fernando.

Fernandinho clipped the post in a rare City chance, but Real dominated as Bale hit the bar and Joe Hart saved from Luka Modric and Cristiano Ronaldo.

Real saw out the win to meet Atletico Madrid in the final later this month.

The English side knew they potentially only needed one away goal to progress, but appeared reluctant to go for broke in the final stages - despite being encouraged to attack by the vocal 4,500 away supporters.

The home side's only other moment of concern came in the closing minutes when Sergio Aguero's speculative effort flew on to the roof of the goal.

Now they will meet Atletico at Milan's San Siro on 28 May, in a repeat of the 2014 final which Real won 4-1 after extra-time.

No dream goodbye for Pellegrini

City started the second leg knowing there would be no potentially awkward meeting with incoming manager Pep Guardiola in the final, his Bayern Munich side having fallen in their last-four tie against Atletico on Tuesday.

Now Pellegrini, like his Spanish successor at Bayern, will end his three-year reign without a dream goodbye in the San Siro.

Nevertheless, the Chilean will always be remembered for taking the Blues into the Champions League knockout stage for the first time.

Pellegrini finally succeeded where predecessor Roberto Mancini failed, but City's demanding owners will be expecting Guardiola to take their club into the latter stages as a minimum requirement.

Judging by their performance over the two legs against Real, the former Barcelona coach may decide his inherited squad needs an injection of world-class talent to regularly compete with Europe's elite.

For large periods, City lacked pace and energy against the Spanish title hopefuls - and, crucially, offered little attacking threat.

Key centre-back Vincent Kompany's early departure through injury left them lacking defensive organisation, while Yaya Toure's return failed to add any intensity to a midfield lacking bite in the Bernabeu.

And mustering only one shot on target in each leg was a telling statistic.

City's hopes hit by Kompany injury

City suffered a cruel blow inside the opening 10 minutes when skipper Kompany trudged off, a familiar sight this season.

The Belgium centre-half's miserable luck with injuries continues, and the English visitors looked far less assured at the back without their leader.

His departure disrupted an encouraging start by the visitors - and they were punished shortly afterwards.

The away defence, still regrouping, stood off a Madrid attack down the right, allowing Bale to run behind them on to right-back Carvajal's pass and thump the ball in off Fernando's outstretched foot.

Hart rightly described the winner as "lucky", but in truth City could have conceded more over the two legs.

At the Bernabeu, the home players - particularly Bale and the returning Ronaldo - often ghosted between centre-halves Eliaquim Mangala and Nicolas Otamendi too easily.

England keeper Hart, who saved City from losing the first leg, again came to the rescue to give City hope until the final whistle.

Should Real have been reduced to 10 men?

Raheem Sterling has struggled to live up to his £49m price tag since arriving from Liverpool last summer, but the England international's introduction as a second-half substitute provided a little more spark for the visitors.

The attacking midfielder was scythed down by home substitute Lucas Vazquez, who lunged in with an awful challenge close to the corner flag.

Vazquez was booked by Slovenian referee Damir Skomina - but was lucky to escape a red card for the 83rd-minute tackle.

Had he been dismissed, the numerical advantage might just have given City a better chance in the final 10 minutes.

Bale 'turns a corner' in Spain

While all the pre-match talk centred around the threat to City from Ronaldo, Wales forward Bale again demonstrated his emergence as one of Real's most important players - little over a year after he was jeered by fans.

"I feel like I am maturing," said the 26-year-old, who cost a world-record £85m fee when he joined Real in September 2013.

"My Spanish is getting better and I'm integrating more with the team. I feel like I have turned a corner in that sense and I'm enjoying my football here."

What's next?

City must put this disappointing defeat behind them and focus on making sure they play in the Champions League under Guardiola next season.

The Blues currently occupy the Premier League's fourth and final qualification spot, four points ahead of fifth-placed Manchester United who have played a game fewer.

Pellegrini's side host third-placed Arsenal on Sunday - a key game in deciding the top four.

Meanwhile, Real Madrid have a Spanish title race to concentrate on. Zinedine Zidane's third-placed side trail both Barcelona and Atletico by one point with two rounds of matches left.

The stats you need to know

Real Madrid have reached their 14th European Cup/Champions League final, a record in the competition.

It will be the third time in the past four years that the Champions League final has been contested by teams from the same nation.

The Spanish giants have won all six of their Champions League home games this season, keeping a clean sheet each time.

Cristiano Ronaldo played in his 17th Champions League semi-final - the joint most in the competition along with Xabi Alonso.

Sergio Aguero has failed to score in his past five Champions League games - his joint-longest drought in the competition with Manchester City (also between November 2011 and December 2012).

Aguero has not managed a shot on target in his last 522 minutes of Champions League action.

Keylor Navas has kept 11 clean sheets in his 12 Champions League appearances, including all six at the Bernabeu.

Manchester City have been eliminated by Spanish opposition for the third consecutive Champions League season.

For the third season in a row, a manager has reached the Champions League final in his first season in the competition (Diego Simeone 2014, Luis Enrique 2015, Zinedine Zidane 2016).

(BBC)