Mourinho's team selections had been questioned by the British press after last month's shock 2-1 home defeat to Basel in their European opener and the Portuguese coach cut short his pre-match news conference on Monday irritated by further questions on the issue.
While Mourinho looked impassive after watching his side, he was clearly happier about his team's position in Group E where they are now second on three points behind Germany's Schalke 04, who won 1-0 against Basel on Tuesday to move onto six.
"We needed to clean up what we did at home (against Basel) and we did it with a good performance," he said of the 2012 Champions League winners who failed to advance from the group stage last season.
"If we didn't win today we were in trouble. We finish the group with a game at home (against Steaua), that is an advantage, but at this moment I don't want to think about finishing first, I want to think about qualifying for the next stage."
Brazil midfielder Ramires scored twice, either side of an own goal from Daniel Georgievski, Frank Lampard got the fourth, while German winger Andre Schurrle and Spain's Juan Mata were outstanding in a game Chelsea could have won by a bigger margin.
"Schurrle was fundamental. We identified what we had to do to penetrate their defence He was the man for that," said Mourinho, who had publicly criticised the newly-arrived German after the Basel defeat.
"We scored four and probably could have scored six or seven because we played really well.
"I put a lot of pressure on the players for this game, and they coped well with that pressure," he added.
"In attacking areas we had beautiful moments in the game but everything started at the back. (Branislav) Ivanovic, David Luiz, who made zero mistakes all game, (John) Terry and (Ashley)Cole gave us stability and from there the team could cope with the situation."
Mourinho even maintained his optimism when talking about Fernando Torres' knee injury after the Spain striker had limped off in the 11th minute.
"Our doctor is confident it is not a big injury like (Marco) Van Ginkel's, but we will have to wait for the scans," he said following the news that Van Ginkel could miss the rest of the season with ligament damage.
Next up for Chelsea are back-to-back matches against Schalke who will prove a much sterner test for the Londoners than the Steaua who are bottom of the table having lost both their matches and conceded seven goals.
"Now we have three points from two matches. Basel lost and now have the same points as us, so Schalke have the advantage, but we now have two fixtures against them. We are going to do it (qualify for the last 16)," Mourinho said.