Djokovic won the tournament in 2011, 2014 and 2015 but has failed to make it beyond the quarter-finals in the past two years.
Djokovic, who was sitting in a small press room without mics and just in front of a few journalists (most of them were waiting in the main press room), said he doesn't know whether if he will play Wimbledon next month.
"I don't know if I am going to play on grass", said the Serb.
"It was the best moment of my life", Cecchinato said.
"Maybe I'm sleeping. It's fantastic, it's unbelievable for me".
World number 38 Khachanov has now lost at the last-16 stage at Roland Garros twice in a row, while Zverev ended his wait for a maiden major last-eight appearance at the 12th attempt. "It's awesome", said the 25-year-old Cecchinato.
The smash to end it wasn't his only one of the match.
And Djokovic woke up, blazing through the third set as Cecchinato looked out of sorts. As the score indicates, that was far less compelling, in part because Zverev felt pain in his left hamstring 10 minutes into the match and wound up having his leg taped by a trainer. I struggled from the beginning. "Because if I played just to stay in points, I could never beat Novak".More news: Scooter Libby, Sheriff Joe Arpaio and others pardoned by Pres. Donald Trump
Verdasco saved four set points in the opener on his way to a 7-6 (7-4) 6-2 6-4 triumph, with Dimitrov - knocked out in the third round for a second successive year - declaring afterwards he will be taking a break from the sport.
Yet Djokovic won the third set at a canter, and a suddenly frustrated Cecchinato was hit with a point penalty for unsportsmanlike conduct.
Asked if he was back, however, Djokovic was blunt.
Former world number one Djokovic will face Italian surprise package Marco Cecchinato in his 40th major quarter-final.
In the first round at Roland Garros, he dropped the first two sets against Marius Copil, a player ranked 94th, before coming all the way back to win 10-8 in the fifth. Analyzing the match, Djokovic added: 'He played awesome and credit to him.
Djokovic, a former world number one and 12-time Grand Slam title victor, had previously only been beaten by a player ranked lower than 25-year-old Cecchinato at the majors on two occasions - Marat Safin at Wimbledon in 2008 when the maverick Russian was at 78 and 117th-ranked Denis Istomin at last year's Australian Open.
Zverev said he will undergo an MRI to discover the seriousness of his injury. There was no way for me.
After an even start full of high quality ball-striking, Thiem broke serve at 3-3 and quickly got on top, stretching his opponent all over Court Philippe Chatrier.
"Sometimes you have to battle to get the win and that's what I did today".