"The team is doing pretty well, but like everyone we have to deal with injuries. There are some physical problems that are slowing our work down," said Mourinho.
"In the first half we ran a few risks against an aggressive and organised Livorno. After the break we started better, found the goal and controlled the situation.
"When we double our lead, the match was essentially over."
Mourinho was quick to praise veteran midfielder Patrick Vieira.
"This was the best game Vieira has played under me. If he is in good shape and can work hard, he is a wonderful player.
"Today he put in an excellent performance and in the second half our system did not force him to look out for the opposition wingers, so he was able to play the way he prefers," he added.