City are 15 points behind Premier League leaders Manchester United.
"You always want to go for the titles and you always want to go for the top," Kompany told the Manchester Evening News.
"I've experienced it in the same way as every other player. I've wanted our team to do well.
"In football, ultimately, you always have to have a winner and a loser so I think that we'll learn from what happened and we'll grow stronger again. We still have a good run in the FA Cup."