"I am not aware of any senior players going to the owners (to express their frustration at results). That is news to me. A lot of it has been speculation, no foundation," Shakespeare told reporters on Friday.
"I've not had one problem with the players. There was a lot of frustration because of the results but he (Ranieri) had not lost the dressing room."
Five straight league defeats have left Leicester, who won the title last May with 5000-1 odds against, just above relegation and the club's Thai owners fired Ranieri, weeks after saying he had their "unwavering support".
Shakespeare also played down reports suggesting his relationship with Ranieri had deteriorated in the weeks before the dismissal.
"My relationship with Claudio has been perfectly fine, I've never had a problem with him, he's never had a problem with me," Shakespeare said.
"I always feel sorry when people lose their jobs. I'm not aware of the club having spoken to any candidates. Do I think I can do the job? Yes. Does it faze me? No."
Leicester are only a point and a place above the bottom three and Shakespeare hopes to rebuild confidence, starting with Monday's match against fifth-placed Liverpool.
"Confidence can go very quickly but it can come back very quickly. My aim is to restore that confidence quickly," he said.
(Reporting by Shravanth Vijayakumar in Bengaluru; Editing by Louise Ireland)
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