The reigning champions are third in the table having taken two points from a possible 12 since Wilkins left and face a tough trip to Tottenham on Sunday.
"I honestly believe they'll turn it around," Wilkins, who was sacked on 11 November, told BBC Radio 5 live.
"The next three games are a very, very important period for Chelsea."
Their most recent match saw them beaten by Marseille in the Champions League on Wednesday night, although they had already qualified for the knockout stage.
"When you're used to winning all the time it's a kick up the backside when it doesn't all go your way," said Wilkins, who joined Chelsea's coaching staff for a second time in 2008.
"These things can happen and that's what makes our game the best in the world. The results will take care of themselves.
"Then it's United at Stamford Bridge and then Arsenal, so these three games are of paramount importance and if they come out with a decent batch of points they'll be right up there again.
"It will be a very difficult period for Carlo if those results weren't to go as he would like."
Ancelotti has come under pressure during Chelsea's disappointing sequence but on Friday the Italian insisted he does not fear for his job after speaking with owner Roman Abramovich.
Many have pointed to Wilkins' dismissal as the key factor behind the recent on-field problems, yet the former England midfielder was quick to suggest there was no correlation.
"That's all it is [a coincidence]," he stated. "I know the quality that's in the dressing room. They've had a few injury problems and suspensions.
"The injury problems aren't coming to normal footballers, they're coming to the likes of Frank Lampard - 20 goals a season from midfield for the last six or seven years - and Michael Essien, suspended for three games.
"These are two powerhouses who would get into the midfield of any team in the world. They're going to be sadly missed."
Wilkins described Ancelotti as a "very good friend" and pointed out that the club's decision to relieve him of his duties was not driven by the manager but Abramovich.
"There was no real explanation as to why I've been dismissed, only that Roman wanted some change," continued Wilkins.
"When you've spent Â£750-800m you're entitled to make that change when you wish to make it and unfortunately I was the guy that went.
"But that's his prerogative, he made that decision and I wish them the best of luck.
"It came as a bit of a bolt out of the blue but never be surprised by what happens in football because these things do rear their ugly head now and then.
"Unfortunately I was on the receiving end of it. I'm OK now, I'm over it and just cracking on."