City are still waiting to learn the extent of his calf problem but manager Roberto Mancini expects to be without the 25-year-old for Sunday's trip to Swansea and the return against Sporting.
Mancini said: "I hope that for Vinnie, the injury will be short.
"When you have a calf (injury), it can be a big problem. I hope he can recover in 10 days, two weeks maximum.
"We will see how it is in another one or two days."
Kompany added on Twitter: "Still too early for updates on the injury. I appreciate your concerns. We have to turn focus to the Swansea game now. Team will be fired up."
Mancini at least said he does not think groin soreness experienced by Kompany's replacement on Thursday night, Joleon Lescott, "was a big problem".
England right-back Micah Richards is also expected to return after again being rested due to a knock suffered on international duty last week.
Mancini said: "I didn't take a risk with Micah because Pablo Zabaleta is injured. Micah will play on Sunday."
City are now staying in Lisbon to train in warm weather for the next two days before travelling directly to south Wales.
It may also give them time to reflect on a below-par performance which left them needing to overturn a deficit to reach the last eight.
Brazilian defender Xandao scored the only goal at the Estadio Jose Alvalade, brilliantly backheeling past Joe Hart after the goalkeeper had produced a double save from both him and Matias Fernandez prior to that.
City had chances through Aleksandar Kolarov and Gareth Barry but it was not until the late introduction of Mario Balotelli, who almost set up David Silva, that City looked close to their best.
Hart had earlier produced two fine saves to keep them in the game.
Mancini, however, felt his side had been unlucky.
The Italian said: "It wasn't a surprise because anything can happen in football, but I don't think we deserved to lose.
"We didn't play very well but could've scored, then conceded a goal - so that is it.
"We have another 90 minutes and I think it will be a different game. We still have a big chance."
Sporting coach Ricardo Sa Pinto said: "I have a lot of respect for Mr Mancini, as a player and a coach, but I have a different opinion."