Gareth Bale's cross deflected off Fernando to give Real a 1-0 aggregate victory and set up an all-Madrid final with Atletico in Milan on 28 May.
Pellegrini's side had just one shot on target in the Spanish capital.
Asked if he regretted his team's approach to the game, the Chilean said: "No. I think we worked very well."
Pellegrini felt his side did not deserve to lose and said the hosts were "very lucky" with the deflection that gave them their goal.
He added: "Real Madrid could not create chances, but after that work you have to create and have players who can do work in the final third but we couldn't."
Real dominated for much of the game and had 15 shots on goal, five of which were on target.
City rarely troubled the hosts, going closest when Fernando hit the outside of the post, while Sergio Aguero's late long-range shot landed on the roof of the net.
City captain Vincent Kompany was substituted with a suspected groin injury in the 10th minute.
The Belgium defender, 29, has started just 14 games in the Premier League this season.
Pellegrini said: "It is not the best way to start a game.
"However, I don't think we had a problem defending with or without Vincent.
"We recovered the ball well, we tried to press high and did it but you have to make the difference with the ball."
Pellegrini added he expects to know more about Kompany's injury on Thursday.
'A special season'
City are fourth, four points ahead of Manchester United, who have three games remaining to their rivals' two.
"It has been a special season because we reached the semi-final," said Pellegrini, who will be replaced by Bayern Munich boss Pep Guardiola this summer.
"It was a very close game but we must finish now in the domestic game to try and qualify for the Champions League again."
City goalkeeper Joe Hart, who made a number of excellent saves in both legs of the semi-final, believes the club will learn from the experience.
He said: "There's not a lot we can take from this game but in the Champions League this season we have grown and shown some good moments and we have to take that into next year.
"It's not a proud moment losing a semi-final when we like to think we could have done a lot better.
But we didn't and we are out."