They are seventh with nine points from their opening five games, and lost their opening Europa League game.
“I feel that some individuals probably feel the pressure and responsibility too much,” said Mourinho.
“We have to improve, no doubt, individually and collectively. And that’s my job.”
The Red Devils won the Community Shield and their opening three league games under former Chelsea and Real Madrid manager Mourinho, who replaced the sacked Louis van Gaal in the summer.
“We started the season very well with winning the Community Shield and three victories in a row in the Premier League, the best start that a new manager has had at Manchester United I think,” said Mourinho.
“But was I thinking that my team was ready, perfect, unbeatable? Not at all.
“I was completely aware that we were not perfect, with lots of players who are not end products and can make their own mistakes.”