Winger Mkhitaryan scored in United's 1-0 Europa League last 32 second-leg win over Saint Etienne, but limped off with a hamstring problem after 25 minutes.
Carrick was also substituted just past the hour mark after hurting his calf.
"Honestly, I don't think Mkhitaryan is fit for the final. I think him and Michael are both out," said Mourinho.
"You can be injured leaving your house, you can be injured in the garden. You never know when and why.
"Obviously they are important players for us and not to have them both for the final is complicated but I think Marouane (Fellaini) and Bastian (Schweinsteiger) - two players who are normally not playing too much - is a good answer.
"I don't say they will definitely miss out, I just say what I feel. It's three days before the final. Even if it's a minor injury I think three days is no time."
United beat Saint Etienne 4-0 on aggregate to move into the last 16 of the Europa League and are also in the quarter-finals of the FA Cup.
Mourinho's side beat Leicester to win the Community Shield in August, but Sunday's EFL Cup final at Wembley is the 54-year-old's first chance for a major trophy with United.
Manchester United manager Jose Mourinho expects midfielders Henrikh Mkhitaryan and Michael Carrick to miss Sunday's EFL Cup final against Southampton.