Reports had claimed that some senior players questioned Villas-Boas' team selection and tactics in a squad meeting that owner Abramovich also attended following the club's 2-0 defeat to Everton two and a half weeks ago.
Further reports of unrest within the Chelsea camp have emerged since, piling more pressure on the under-fire Blues manager, who admitted for the first time that he fears for his future at the west London club.
Cech moved to quash reports of disharmony in the Stamford Bridge dressing room today, however, telling Czech website isport.blesk.cz: "Everyone has been talking about a meeting between the team and Abramovich. The truth is elsewhere and the picture of that meeting was distorted.''
Speculation over 34-year-old Villas-Boas' future has been rife in recent weeks, mostly thanks to his team's poor form.
Chelsea have won twice in their last eight matches, although their latest win - a 3-0 victory over Bolton on Saturday - moved them to within seven points of third-place Tottenham.
Cech accepts that speculation will continue about the club while results are not going Chelsea's way.
"The club is under constant pressure media. That's the problem,'' the Czech Republic international added. "There is a lot of speculation and nonsense, but we have to live with it.''
Chelsea have a good chance to keep up the pressure on Spurs and fourth-place Arsenal over the next two weeks with games against West Brom, Birmingham in the FA Cup, and Stoke.
Cech insists that there is now a positive atmosphere at the club following Saturday's home win over the Trotters and the goalkeeper is confident that a good run of results will now follow.
"The mood always derives from results so the mood is better,'' Cech said.
"Tottenham lost at the weekend. We can to get closer and play for third place. We still have a chance to finish third but our aim is to finish fourth as the worst case scenario. That's clear.
"I still believe things will turn for the better and our season will be successful.
"Everybody has been doing their best to change the situation. But what happens in training we are not able to take into competitive games. People can hardly say we're not putting in enough effort.''