Mourinho had acknowledged before kick-off that his team needed a good result after losing at home to Basel in their opening Group E game, and they bounced back in style in Romania.
Ramires scored twice and there was also an own goal from Daniel Georgievski and a late Frank Lampard strike on a morale-boosting night for the Blues.
"I think we are going to qualify," Mourinho told Sky Sports. "Today's result is important because if we don't win we are under pressure.
"We have to control the situation and make points against Schalke and then beat Basel and Steaua."
Mourinho was full of praise for his side with winger Andre Schurrle producing his best performance since his summer move from Bayer Leverkusen.
"The result is very good. The points and the goals also," he said.
"From the first minute it was very good. From the first minute we kept control of the game. We played good football with intelligence and maturity.
"We needed to clean what we did at home (against Basel) and we did it with a good result and performance.
"Now we are not in a dramatic situation, we are in a close situation."
Fernando Torres had to go off after just 11 minutes with a knee injury that will need to be assessed, but Mourinho is hopeful that he will not be out for too long, having already lost Marco van Ginkel to a long-term knee problem this season.
"We have to wait for tomorrow for a scan," he said. "I hope it is not dramatic like Van Ginkel.
"I thought it was an ankle injury when he slid in. Hopefully it is not so dramatic."
Mourinho also defended the Football Association's decision not to retrospectively punish Torres following an incident involving Jan Vertonghen during the weekend's 1-1 draw at Tottenham.
"It doesn't surprise me," said Mourinho, who offered another thinly-veiled barb at Vertonghen.
"The FA represents English football and in England they never punish on emotion.
"They punish when you don't respect the integrity of game by simulating."