"Many players weren't satisfied or working hard and there was also an internal communication problem," said Abidal.
"The relationship between the coach and the dressing room has always been good but there are things as an ex-player that I could smell. I told the club what I thought and we reached a decision (on Valverde)."
Messi, however, hit back at Abidal in an Instagram post, circling an image of the sporting director's quote.
"Sincerely, I don't like to do these things but I think that people have to be responsible for their jobs and own their decisions," Messi wrote.
"The players (are responsible) for what happens on the pitch and we are the first to admit when we haven’t been good. The heads of the sports department have to take their responsibilities too and above all own the decisions they make.
"Finally I think that when you talk about players, you have to give names because if not, it makes everyone dirty and gives air to things that are said which are not true."
Abidal and Messi played together at Barcelona between 2007 and 2013, with the French defender returning to the club after retirement to become sporting director in June 2018.
In his interview with Diario Sport, Abidal also said he thought Messi was happy at the club and a new contract for the Argentine talisman was currently being negotiated. (Reporting by Rik Sharma Editing by Toby Davis)