The Reds forward grabbed the right arm of the Serbian before biting him during the second half of their 2-2 draw at Anfield on April 22.
Suarez was subsequently banned for 10 games for violent conduct by the Football Association, but Ivanovic has played down the incident and said that he wants to move on.
"The next day we talked on the phone and I accepted his apology," Ivanovic told Serbian newspaper Vecernje Novosti.
"When it happened I was really surprised and of course shocked, but when the match ended, it all cooled down. I almost forgot about everything. I didn't attack him for what he done but I also didn't defend him.
"But I forgive him. For me, that can happen. But I really don't care too much."
Liverpool did not appeal against the decision to ban Suarez, meaning that the former Ajax man will be out of action in the Premier League until late September.