City was beaten 1-0 at the Estadio Jose Alvalade in the Europa League last-16 clash and lost the influential Belgian defender after just 12 minutes.
"We have to wait one or two days to know the exact extent of his injury, but it is a problem with his calf," Mancini told reporters after the match. "I hope to have Kompany back in 10 days or two weeks, but we have other solutions."
The Italian was also adamant that City can get back into the tie, given the narrow nature of the deficit.
"This result was not a surprise, anything can happen in football," he said. "I do not think we deserved to lose. We did not play well, we had chances to score, but we didn’t. We have bigger chances to go through. It will be a different game in Manchester. When we have chances to score, we will score.
"I don’t think Sporting had a lot chances to score. We played like this because Sporting played with all their men behind the ball for all 90 minutes; they wanted to hit us on the counter.
"We played slow sometimes because we found 10 players behind the ball. We had more chances to score than Sporting.
"We did not underestimate them. Every game is difficult and different, we tried to play good football, sometimes we can, sometimes we can’t. We did not underestimate them. Football is strange. We have another game and we have more chances to win the next game."
Defender Gael Clichy was forced to occupy an unfamiliar role on the right-hand side of defense but his boss praised the Frenchman's display and that of goalkeeper Joe Hart.
He said: "He did a good job, right-back is not his position, but we had to choose, or Gael or Stefan [Savic], because Sporting have quick strikers and quick wingers, but he had a good performance. Joe is a fantastic keeper, this is his job, and I hope he will continue to improve."
Mancini also dismissed concerns over the absence of Micah Richards and insisted Thursday's loss should not affect City's Premier League form.
"He [Micah] is OK but I did not want to take risks for Sunday's game," said Mancini. "I’m not worried [about Swansea], it’s a different competition, I am sure we will go through in the Europa League, and that Sunday it will be a different game. The game against Swansea will be a very difficult one, they are one of the teams who play the best football in the Premier League."Follow GOAL.COM USA on