After guiding Leicester to one of the most unlikely title victories last year, Ranieri was fired on Thursday with the Foxes mired in a relegation battle. They are now 18th in the table, two points above bottom side Sunderland.
"There is speculation I was involved in his dismissal and this completely untrue, unfounded and is extremely hurtful!" Vardy wrote in an Instagram post on Saturday alongside a photo of Ranieri.
"The only thing we are guilty of as a team is under-achieving which we all acknowledge both in the dressing-room and publicly and will do our best to rectify," he added.
Vardy scored 24 Premier League goals last season to spearhead Leicester's extraordinary triumph after starting the campaign at odds of 5,000-1 to win England's top-flight title for the first time in their history.
"Claudio has and always will have my complete respect! What we achieved together and as a team was the impossible! He believed in me when many didn't and for that I owe him my eternal gratitude," Vardy said.
"I wish Claudio the very very best in whatever the future holds for him. Thank You Claudio for everything."
Vardy's post came after goalkeeper Kasper Schmeichel also denied reports that players led a revolt against the 65-year-old Ranieri who said goodbye to the Leicester squad on Saturday morning.
"There's absolutely no truth in that whatsoever," The Dane told the BBC. "We are players, we can only affect on the pitch and we haven't done that."
Leicester are owned by Thai businessman Vichai Srivaddhanaprabha who is the club chairman.
"What I can say is our owners are very hands on. They are in and around the club. They've been here all the time, they come to practically every game and they speak to all the players regularly," Schmeichel said.
"They're successful businessmen and they're not going to allow themselves to be influenced by any players."
Leicester host Liverpool on Monday.
(Reporting by Tom Hayward, editing by Ed Osmond)
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