Roma were 2-1 ahead before collapsing in the first-leg of their Europa League semifinal at Old Trafford.
“It's a heavy defeat, obviously. I think we had a good first half, but didn't hold out in the second," Fonseca told Sky Italia.
“We lost three players and had no more substitutions. Amadou Diawara and Chris Smalling were struggling, but I couldn't replace them. It was a very difficult second half for us.
“It's hard to explain how we did that first half and then came out for the second with no aggression, making a lot of mistakes, leaving spaces.
“When they scored the third goal, the team didn't have the mental strength to get back on their feet. It's difficult to play against a team like Manchester United anyway, let alone when we can't make any substitutions.
“I think it's very positive that we reached the semi-final and played this first half in Manchester. That proves the team can compete. However, we got everything wrong in the second half.
“I don't believe it was a tactical problem. As we showed in the first half, we allowed Manchester practically no chances. Our choices were logical ones.
“We lost important players early on and then didn't have the mental strength in the second half. I think that was the issue."
Considering they were exhausted and leading 2-1, should Roma not have tried to park the bus in the second half?
“We tried to do that, but when we have the ball, we must try to attack. I saw it as a psychological issue, not reacting to the third goal. We were by no means out of the running at 3-2, but at this moment the team is struggling and we didn't react. Diawara and Smalling were having so many physical issues, I couldn't change them.
“I don't want to create alibis, I am always the ultimate one responsible and of course I do not want to shy away from those responsibilities. I am just describing what happened."