Mourinho watched his side cruise to a 3-0 win over Basel at Old Trafford in their Group A opener on Wednesday, though he was not impressed with United's performance, criticising them for not doing a thorough and professional job.
Chelsea were the other English side in action on matchday one, thumping Azerbaijani newcomers Qarabag 6-0 at home, while Manchester City and Liverpool face Feyenoord and Sevilla, respectively, on Thursday.
Mourinho does not rate the chances of any of them winning the competition particularly highly, though, suggesting that while the Premier League sides are giving the Champions League their all, Madrid, Barca and Bayern are just "warming up" and benefit from having a winter break.
He told reporters: "I think the Champions League for these teams [big European sides] that you are speaking, and for Real Madrid, Barcelona, Bayern, I think for these teams the Champions League starts in February.
"Now is just the warming up and in February when us English teams, we are trying to survive after the winter period, they will be fresh and ready after these warm-ups.
"For them this is a warm-up. I think we [English teams] are in the second level. And the second level is 'let's qualify'.
"Let's get the points to qualify for the knock-out phase and when we do that, if we do that, let's enjoy playing against the big guys."