The Uruguay international has also said he will submit a written transfer request by the end of the week if the Anfield club continue to block a potential move to Arsenal.
Suarez, in interviews given to the Daily Telegraph and The Guardian, said he believes a clause written into the contract he signed last summer entitles him to a move.
Suarez said: "Last year I had the opportunity to move to a big European club and I stayed on the understanding that if we failed to qualify for the Champions League the following season I'd be allowed to go.
"I gave absolutely everything last season but it was not enough to give us a top-four finish - now all I want is for Liverpool to honour our agreement."
Liverpool have rejected two bids from Arsenal - of £30 million and £40,000,001 - for Suarez this summer.
Suarez understands the Gunners' unusual second bid of £1 over £40m triggered a release clause, but Liverpool believe they must only inform the player of an offer beyond that mark and negotiate if they wish to sell.
Suarez said: "I don't feel betrayed (by Liverpool) but the club promised me something a year ago just as I promised them that I would stay and try everything possible to get us into the Champions League.
"They gave me their word a year ago and now I want them to honour that.
"And it is not just something verbal with the coach but something that is written in the contract. I'm not going to another club to hurt Liverpool."