While Juventus lost to Lyon on away goals and an aggregate of 2-2, despite winning the second leg 2-1 at home, Real Madrid was defeated by English giants Manchester United 2-1 and an aggregate of 4-2.
"We have prepared for the match and we are ready to take on everything that Napoli will throw at us".
Barcelona coach Quique Setien said after the match that he didn't think the injury would be a problem for Messi.
Despite Barcelona securing victory Messi did not let the incident slide at the final whistle, when he was seen wagging a finger at Cakir and appearing to refuse a fist-bump from the official.
Napoli, whose own league season only finished last weekend, should have had the advantage of rhythm but a disastrous first half left them with too much to do.
Barcelona will meet Bayern Munich on Friday in the quarterfinals to be played in Lisbon in a "bubble" format of tight security to prevent a coronavirus outbreak from derailing the competition's finale.
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Napoli began an eventful first half by hitting the post as Dries Mertens went close with a miskicked half-volley, only for Lenglet to head in for Barca from Ivan Rakitic's corner after nine minutes.
The disappointment didn't last long as Messi's quick thinking saw him nip in behind Napoli defender Kalidou Koulibali who accidently kicked him on the Achilles heel to concede a penalty.
Messi made it two after a barnstorming run in which he fell to the ground only to dart back up and bundle his way through three Napoli defenders before curling into the far corner.
"A clear penalty", MARCA's referee expert stated.
Luis Suarez put the home side 3-0 in front, after a foul on Messi, but Lorenzo Insigne handed the Serie A side a lifeline as he tucked home from the spot. Barca were relieved to hear the whistle.