United were forced to draft centre-half Eric Bailly into the starting line-up moments before the game after Chris Smalling suffered an injury during the warm-up.
Mourinho said the club's difficulties with injuries had been a long-term issue.
"First of all, we have lots of problems related to physicality, we have lots of players that I could consider injury prone, because some of our players are always injured and is not with me, was before me," he told reporters.
"If you look to the stats with Mr (Louis) Van Gaal and before Mr Van Gaal with David (Moyes), if you look to that period you have players that are permanently injured, when you are permanently injured, physicality is very difficult to get," he said.
Liverpool's speed and aggression allowed them to dominate United in the opening period of the game and Mourinho said much of that superiority came from the physical qualities of Juergen Klopp's players.
"There are qualities that a player has or doesn't have. You cannot improve, you cannot make them have. I give you an example: (Andy) Robertson, (Sadio) Mane, (Mohamed) Salah, (Georginio) Wijnaldum, (Naby) Keita, Fabinho, they are physical players, on top of that they are good players technically, I also have lots of good players, technically, but we do not have many players with that intensity or physicality.
"So when the game has high levels of intensity is difficult for us. Our first 20 minutes was difficult for us," he added.
Mourinho was careful to praise the work-rate of his players at Anfield.
"I am really, really happy with the players I had on the pitch with their attitude, with their effort, I am more than happy. Because I am more than happy I assume the responsibilities of the defeat and I want them to be hidden behind me," he said.
(Reporting by Simon Evans, editing by Ed Osmond)
