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.
It was a privilege to work with these guys, they've got some of the top players in world football playing there and they shouldn't be languishing where they are at the moment
"When you've spent £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."
Wilkins, 54, enjoyed a distinguished playing career with the likes of Manchester United, AC Milan, QPR and Rangers after making his Chelsea debut as a 17-year-old in 1973.
He managed QPR and Fulham in the mid-1990s before two spells as Chelsea's assistant coach, helping Gianluca Vialli in 1999 and 2000 before rejoining in September 2008 under Luiz Felipe Scolari.
"It saddens me immensely because it's a place where I thoroughly enjoyed working and to work with the quality of guy [Ancelotti] that I was able to work with was exceptional," added Wilkins.
"We had such a lovely ambiance in which to work that I miss it immensely. In the first week I was bashing the walls and kicking doors but the disappointment has gone now.
"I sincerely hope they buck up and win. It was a privilege to work with these guys, they've got some of the top players in world football playing there and they shouldn't be languishing where they are at the moment."
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