The west London team, who have spent more than $200 million on players since Roman Abramovich's takeover last July, qualified by virtue of an own goal in the first leg of the knockout round at VfB Stuttgart two weeks ago.
On Tuesday, they were lucky to escape with a 0-0 draw in the second leg after sustained Stuttgart attacks.
"It's strange, we played better in Stuttgart a fortnight ago," Ranieri said. "Maybe we were looking at what could be achieved and were too nervous."
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"Of course, it was tense but I enjoy this emotion," he said with a wide smile after Chelsea reached the last eight in Europe's premier competition for the second time.
Four years ago, under Ranieri's compatriot Gianluca Vialli they were beaten in the quarter-finals by Barcelona.
"We know it will not be easy but we want to continue," Ranieri said.
France captain Marcel Desailly, one of the few survivors of Vialli's squad, came on as a substitute to make his first appearance for Chelsea since January 18.
Ranieri praised the towering defender's performance and said fullback Glen Johnson, who was carried off in obvious pain, had a very swollen left ankle.
Stuttgart coach Felix Magath said that over the two matches his side had not been second best.
"The two teams were very balanced. I think Chelsea had a little bit of luck," he said. "It is clearly hard to go out after playing 160 minutes one down because of an own goal."
Magath said his side had to do something about their inability to score. "We have a great deal of talent in the team but we should be able to translate that talent into goals."