Mourinho, who steered the English champions to a 2-0 win over his former club Porto 2-0 on Wednesday to finish top of qualifying Group G, said history showed the favourites often find it hard to excel in Europe's most prestigious club competition.
"It's obvious a team struggling so much as we are is not obviously a candidate to win the Champions League," he told reporters.
"But when we won in Porto in 2004 we were not candidates. When we won with Inter in 2010 we were not candidates. When we were candidates, we lost two semi-finals with Real Madrid, we lost two semi-finals with Chelsea. So let's see."
Chelsea's only triumph in the Champions League, in 2012, came under former manager Roberto di Matteo, when the London side were having a poor domestic season.
Despite retaining the loyal support of the Chelsea fans, who chanted his name throughout Wednesday's game, Mourinho's position at Stamford Bridge has come under intense pressure after his side lost eight of their first 15 English league games this season.
Mourinho paid tribute to his players for playing for a win against Porto when a draw would have been enough to secure qualification for the knock-out phase.
"The thing that I am more happy with, apart from the result, is the fact that we needed one point to qualify and the players they accepted the challenge to play to win and that is not easy when the moment is so bad, the results are so negative and the pressure is so high," he said.
"They were brave to accept that."
Mourinho said Chelsea had enjoyed a bit more luck against Porto than in their English league games after the Londoners took the lead courtesy of a fortunate rebound off Porto defender Ivan Marcano.
"That little bit of luck we never have in the Premier League," he said.
He also said he felt a tinge of regret for eliminating his former team from the competition.
"I would prefer to be here celebrating Chelsea first place and Porto second... but the group put us in this situation."
(Editing by Ed Osmond)
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