The 27-year-old will run out for the Catalan giants after his four-month suspension from all football activity expires, after a £75m deal between the two clubs was agreed.
Suarez was handed the hefty ban for biting the shoulder of Italian defender Giorgio Chilellini during the World Cup - the third time the Uruguayan has been banned for biting in his career.
"He wanted to go and play in Spain, and unfortunately when a player no longer wants to play for you, we need as a club to look at it," ESPN quotes the Liverpool manager as saying. "It was his decision for him to go, he's gone to Barcelona, a club he wanted to play for and now we'll move on.
"I'm not sure if he would have gone regardless of the World Cup. But I never felt that towards the end of the season, and likewise he never said he would give us another year either. He had obviously signed a new deal so we had that.
"But I think we have had great service out of Luis and it's one that we can't worry too much about now, it's done, it's gone and our focus is here."
Liverpool began their pre-season campaign with a 2-1 defeat against Brondby last night.