Chelsea substitute Eden Hazard was the first player to pull a goal back for the Blues, but the United boss did not feel their personnel changes had as much bearing on the game as his own players' problems.
"They [Chelsea] may think that [they changed the game]. If you make substitutions and they work for you, it’s easy to say that. But to be honest with you, I just thought we were running out of legs.
"I detected some tiredness because the players kept giving the ball away. When you see teams giving the ball away as we were doing then you have to understand why. I think the emotions and the intensity of Tuesday took their toll on some of the players, understandably. I've no problems with that but certainly they did feel it in the second half."
Ramires went on to score Chelsea's equaliser and there would have been a winner for the visitors had David De Gea not saved Juan Mata's goalbound effort with an outstretched foot in the 90th minute.
Sir Alex said: "It was a terrific save at an important time because if they'd scored it we would have been out, no doubt about that."
The Reds will instead have a second chance to reach the semi-finals, with a forthcoming replay at Stamford Bridge where United won in the league earlier in the season but lost in the Capital One Cup after extra-time.
"The replay is not a problem for us," insisted the manager. "We’ve got plenty of time for it as we have no European games. I don't know when it's going to be played mind you, probably May because we've got the international break coming up! But the only thing we can say is we're still in the cup."