Fellaini is also set to miss the Premier League match at home to Crystal Palace on Saturday after suffering an injury in last week's win over Southampton, a problem which has come at a bad time for Mourinho.
The Portuguese said: "I won't have Fellaini, I won't have Pogba, we won't have Carrick, so all three are midfield players that we lose for this match.
"So there are not many solutions, but we try not to focus on individual matters or specific areas on the pitch.
"We are going to have a team with quality and balance and try to win the match – that is our objective."
Fellaini was injured after being challenged by Shane Long in the 1-0 win over Southampton last time out, but Mourinho does not expect him to be out for too long.
"It was only when I saw it on TV that I realised Fellaini was very lucky. It could be a much worse situation but in a moment where we don't have Pogba and Carrick he becomes even more important than he always is.
"I do not expect Fellaini to be out for a long time. There is no pressure on him [in the international break] so hopefully he'll be back for us."
Ander Herrera and Nemanja Matic are United's other first-team central midfielders, while the versatile Daley Blind and youngster Scott McTominay could also be options.
Mourinho has also confirmed that defender Phil Jones will miss the game in Moscow.