Wilkins, former manager Scolari's assistant, is in charge for Saturday's FA Cup fifth round tie at Championship side Watford before Dutchman Guus Hiddink takes over for the rest of the season.
Captain John Terry hinted this week that Brazilian Scolari did not have the full support of all the squad.
"There is no player power at this club," Wilkins told the team's website on Friday.
"The results unfortunately have not been what (owner) Roman (Abramovich) wanted and that's why the change of manager."
Chelsea have slipped to fourth in the Premier League, seven points behind leaders Manchester United, who also have a game in hand.
"Whenever any coach coaches a club as big as Chelsea the players that don't play are obviously going to be disgruntled," added Wilkins.
"We certainly don't have a split. None whatsoever."
Wilkins said he was surprised by Scolari's dismissal on Monday.
"I was shocked and disappointed he went because I enjoyed his company, he was a smashing guy," said the former Chelsea and England midfielder.
"I enjoyed working with him immensely but football is a tough game. A couple of results went against us and the decision was made."
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