Kompany took a knock during the second half of the 1-1 draw with Real Madrid and, although the Belgian was able to complete the game, he was not moving freely.
Manager Roberto Mancini can only hope Kompany has not sustained too much damage, particularly with a visit to Chelsea looming on Sunday.
"The opportunity to claim our place at the top of European football will come again," said Kompany on Twitter. "No sad faces, just the hunger to improve."
Mancini is certain he will get the chance to implement the plans too, despite a second successive group stage failure and rejected outright the notion that Sheikh Mansour would deliver a harsh judgment, saying: "No. I don't fear this. Why?
"We still have the Premier League and the FA Cup. If we think we can win the Champions League after two years we are crazy."