Meireles was reunited with former Porto boss Andre Villas-Boas at Stamford Bridge on transfer deadline day after completing a last minute £12m switch from the Reds having handed in a late transfer request.
The Portugal international said at the time that he never wanted to leave Liverpool and he has now claimed that the Blues' Premier League rivals went back on their word.
Meireles said: "All I have to say is that I had one promise at Liverpool which wasn't fulfilled. It's not the only thing to blame. But that's why the Liverpool fans are unsure why I left."
Meireles admitted he was taken aback to discover he had been made available for transfer.
He added: "I was aware that Liverpool wanted to sell me in the summer, which was a bit surprising to me. There's no point touching this subject any more.
"I was a bit surprised, but now I'm just concentrating on my present and future, and that's with Chelsea.
"When Chelsea showed interest, it was like a golden opportunity. I'm here now, it's a new adventure, and I want to do well here."