Messi has lashed out at the club with suggestions that Abidal is using the Barcelona squad as scapegoats for their decision to sack Valverde as head coach.
The record six-time Ballon d'Or winner claims his former teammate should look to shoulder the responsibility and criticised his actions by not stating which players underperformed.
It's been suggested in Spanish media that Messi feels he's been blamed for Valverde's departure, despite publicly backing the former coach in the media on several occasions.
"I honestly don't like doing these things but everyone has to be responsible for their job and take responsibility for their decisions," Messi wrote on his official Instagram account.
"When things don't go well on the pitch, the players are the first ones to recognise as much. Those in the sporting department at the club should also take responsibility for their actions and decisions.
"Finally, I think that when you speak about players, you should have to give names. If you don't, you're dirtying everyone's name and encouraging things which are said which are not true."
The Blaugrana are currently second in LaLiga, three points off leaders Real Madrid after 22 rounds of fixtures.