Benitez launched an impassioned monologue following the holders' 2-0 FA Cup win at ICI City (Middlesbrough) last night, which set up a quarter-final tie with Manchester United.
His criticism sparked suggestions his tenure in caretaker charge could come to an end as soon as today, rather than as scheduled at the end of season.
A Chelsea spokesperson said: "It's business as usual."
The Spaniard stated he would be leaving the club at the end of the season.
Benitez: "I have a title. Someone decided the title would be 'interim'. Why? Just in case?
"If they want to blame me for everything that is wrong and then they say, 'We will put interim just in case', fine, that is your decision.
"I don't agree, but it's your decision and now everybody has to take responsibility. If we are in the Champions League, I will be the happiest man in the world.
"But next year, I will leave anyway because I have finished my contract, so they [his critics] don't need to be worried about me. What they have to do is concentrate on supporting the team.
"I have a contract until the end of the season, that's it, so they don't need to be worried about me.
"It doesn't matter what they say. I am a professional, I have experience and I will do my best.
"But if they carry on in the same way, they have to take responsibility because they are damaging the image of the club and the rest of the fans because people think all the fans are the same.
"The Chelsea fans are really good, they support the team, but if they continue with their agenda, I don't think they do any favours to the team.
"They take time to make banners about me, but they should make banners for the players. This does not help the players."
Meanwhile ... Jose Mourinho is now 4/5 favourite to be the next Chelsea manager after Rafael Benitez confirmed he will leave the club at the end of the season.
Mourinho's time at the Bernabeu is expected to come to an end this summer, having reportedly fallen out with his own players, while maintaining a virtually non-existent relationship with the Spanish media.
The Portuguese holds legendary status at Stamford Bridge having led them to a first Premier League title, while he also boasts three other domestic titles and two Champions League winners' medals.
Everton manager David Moyes is the 4/1 second favourite with his current contract expiring at the end of the season, while Michael Laudrup, whose stock has risen considerably after leading Swansea to Capital One Cup glory, is 5/1 for the post.
Former Chelsea favourite Gus Poyet (7/1) is also considered in the running along with club captain John Terry (16/1) and Borussia Dortmund's highly-rated boss Jurgen Klopp (25/1).