Mourinho was on the brink of being sacked until Chelsea avoided elimination from Europe's elite club competition with a 2-0 win over Porto at Stamford Bridge on Wednesday.
Needing a draw to ensure they made it to the knockout stages, Chelsea got a timely piece of good fortune through Ivan Marcano's early own goal before Willian's second half strike completed a victory that lifted the west Londoners to the top of Group G and eased the pressure on Mourinho.
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The sight of Chelsea owner Roman Abramovich grinning and exchanging high-fives with his entourage afer Willian's goal suggested Mourinho has bought himself a little time to get the Premier League champions back on track.
And the beleaguered Blues boss took heart from the way his players, reportedly mutinous at times during a dismal campaign, responded to the prospect of having to fight to spare him from Abramovich's axe.
"The thing that I'm more happy with apart from the result is the players accepted the challenge of playing to win, even though we only needed a draw," said Mourinho.
"That is not so easy when the pressure is so high and the results are bad in this difficult period.
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"Being in the Champions League is very important. Being here is the minimum we can give to our supporters.
"The results are not as good as the way we are working every day, but after our first goal we were more relaxed and confident."
With Chelsea's domestic form so poor, Mourinho conceded there is only an outside chance they could qualify for next season's Champions League via a top four finish.
That makes winning the Champions League the more likely route back into the competition and, in a transparent bid to take the pressure off his team, Mourinho labelled the Blues as also-rans who would be the preferred choice of all their potential opponents in Monday's last 16 draw.
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Chelsea will face Paris Saint Germain, PSV Eindhoven, Juventus, Roma, Benfica or Gent and Mourinho said: "A team that is struggling like us is obviously not a candidate to win the Champions League.
"The best teams in Europe are in the Champions League. But when we won with Porto in 2004 we were not candidates and when we won with Inter Milan in 2010 we were not candidates.
"When we were candidates with Real Madrid we lost two semi-finals and the same with Chelsea, so you never know.
"I think everybody wants to play us. Everyone team that finished second doesn't want to play Barcelona, Bayern or Real Madrid.
"They want to get us because they think we are the weakest."
With Chelsea languishing just above the Premier League relegation zone and facing a trip to leaders Leicester next, Mourinho isn't out of the woods yet.
If Chelsea are to piece together the kind of winning run that would convince Abramovich not to sack him, Mourinho must get more from Diego Costa, the misfiring Spain striker who played a key role in the opening goal against Porto but generally looked desperately short of confidence.
"It is clear (Costa is struggling for confidence), but it is also clear to see his effort, commitment and great movement which he didn't have in the last couple of months," said Mourinho.
"Yes there is a lack of confidence clearly, but not a lack of effort."
Despite having condemned his former club to the Europa League, Mourinho still earned a vote of confidence from Porto manager Julen Lopetegui.
"Mourinho is one of the best coaches in history. I'm sure he's the right man to continue here at Chelsea," he said.
"I'm sad about the result but we were against a strong team. We had three or four good chances but there were some unlucky situations that changed the result completely."
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