The Premier League outfit crashed out in the final four on Wednesday night after losing 1-0 to the 10-time European Cup winners at the Bernabeu.
Man City lost their captain Vincent Kompany to an injury in the 10th minute, but Pellegrini has insisted that his team's problems were down the other end as they struggled to make inroads in Madrid.
"I think it was a very close game. Neither team created too many chances and Real Madrid were very lucky with the goal." Pellegrini told BT Sport. "It is not the best thing to make a change (Kompany) at that stage, but our problem was that we were not very creative.
"I think we worked the game very well. We tried to recover the ball high and make a difference, but we were not creative and that is why we could not score."
Man City's focus will now switch to the Premier League as they battle to secure a position in the top four.