Mkhitaryan scored the winning goal in United's 1-0 Europa League second leg victory at the Geoffroy Guichard stadium.
Armenian winger Mkhitaryan scored the winning goal in United's 1-0 Europa League second leg victory at the Geoffroy Guichard stadium to give the Premier League side a 4-0 aggregate success in their last 32 tie.
But he limped off with a hamstring problem on 25 minutes, with Carrick also leaving the field just past the hour mark after hurting his calf.
"Honestly, I dont think he (Mkhitaryan) is fit (for the final). I think him and Michael, I think (they're) both out," said a glum-looking Mourinho about their chances of facing Southampton at Wembley on Sunday.
"But this is based on my experience, not based on my medical knowledge, not based on tests and what they have obviously to do tomorrow and after tomorrow."
"I think no chance. I repeat, it's just my experience: a calf, a hamstring, even if minor, minor, some fibres are damaged. I think (they're) out."
Mkhitaryan ghosted between St Etienne's centre-backs to flick home an inviting left-wing cross from Juan Mata on 16 minutes for the only goal of the game to effectively kill any hope St Etienne had of mounting an unlikely fightback having lost the first leg at Old Trafford last week 3-0.
But Mkhitaryan lasted only nine more minutes before trudging off holding his hamstring.
Things got worse as Eric Bailly was sent off for United after two quick bookings and then Carrick also made way with a calf problem, looking dejected as he left the field.
Mourinho again moaned about fixture congestion and hit out at the English Football Association for scheduling their FA Cup quarter-final away to Chelsea on a Monday night, just three days before they will play their Europa League last 16 second leg.
"I feel really surprised that the decision is made before our draw in Europe, because in this moment nobody knows who we (will) play against. Where is the first match and second match?"
"Imagine we play Chelsea on the Monday and we have to go to the second match in Europe in Russia, in Turkey or in Greece. I think once more the (television) interests are going in front of clubs and English football interests and nobody cares about it."
Mourinho also took a swipe at local rivals Manchester City, saying United are too big a club to follow their example from last year when then-manager Manuel Pellegrini played a virtual reserve side in a fifth-round FA Cup clash at Chelsea, losing the game 5-1.
Pellegrini, who made way for Pep Guardiola at the end of the season, gave five teenagers their full debuts in that game but Mourinho said he will run the risk of seeing more players pick up fatigue injuries rather than disrespect the FA Cup.
"I cannot play against Chelsea with the second team. I cannot play against Chelsea with the under-21s like Manchester City did last year," said the Portuguese.
"I cannot do that, we are Man United, we cannot do that. I don't do that as Man United manager, I don't do that to the FA Cup because the FA Cup is not guilty of these decisions."
"Because the FA Cup is beautiful, it's historical. I have to treat Manchester United and the FA Cup in the right way."
"We can't go with the under-21s, so what's happening is the accumulation of matches."
"I'll make some rotation but some boys will have to play in all these matches and if situations like the Mkhitaryan and Carrick ones happen, (then they) happen."