Serie A leaders Inter won 2-0 at Genoa thanks to goals from Zlatan Ibrahimovic and Mario Balotelli but Marco Materazzi went off with a leg injury and Nicolas Burdisso also took a knock.
Cristian Chivu and Walter Samuel were already struggling to be fit for Wednesday's last-16 second leg at United but the performance of midfielder Esteban Cambiasso as a makeshift centre back has eased Mourinho's worries.
"We have faith for the game in Manchester even if I won't be able to sleep because we'll have lots of problems in defence against very strong, attacking opponents," Mourinho told Sky television.
"This team have always come out with their heads held high despite all the problems.
LEADER CAMBIASSO
"In defence, without Materazzi and Burdisso, without me being able to make any more changes, the spirit of the squad has come to the fore. Cambiasso played magnificently as a centre back and on the field he has been a leader."
If the injuries do not clear Ivan Cordoba would be available as well as Nelson Rivas, who started the 0-0 draw with United in the first leg but was substituted at halftime and was poor in Wednesday's 3-0 Italian Cup defeat at Sampdoria.
Mourinho is facing an Italian federation charge after lambasting his Serie A rivals and referees during the week.
AS Roma chief executive Rosella Sensi said the Portuguese had risked inciting violence with his comments and Mourinho was unusually reserved on Saturday, despite controversy over whether Balotelli's goal crossed the line.
"Now I am a coach who does his work and leaves others to do theirs," he said.
