Abidal this week said in an interview with Catalan publication Sport that Barca took the decision to sack Ernesto Valverde after he and his colleagues identified "many players weren't satisfied nor working hard and there was also an internal communication problem".
Messi was disappointed the former left-back chose to tar all members of the squad with the same brush and did not specify names in his remarks.
Barca boss Quique Setien said on Wednesday the six-time Ballon d'Or winner remains happy at the club, with speculation mounting that he could opt to leave at the end of the season.
However, a 1-0 loss to Athletic Bilbao in the Copa del Rey quarter-finals on Thursday was the latest blow for the club, who this week announced Ousmane Dembele will undergo surgery on a hamstring problem that is expected to rule him out of the rest of the campaign.
Speaking after the game at San Mames, Alba followed Messi's lead and claimed Abidal should have known better.
"This club gets enough s*** thrown at it from the outside so we shouldn't be throwing s*** at ourselves. That is the line to follow," said Alba.
"Abidal was a player, he is loved by the fans and that's why he should know what it's like inside the dressing room and how players feel."
Sergio Busquets headed the ball into his own net in the 93rd minute in Bilbao but Alba was pleased with the club's display.
"I think he had a very good game, one of the best of the season. It's a shame we lost at the last minute, but that's football," he said.
"I'm very proud of the team, especially for the level of the game. We have to continue like this.
"It's clearly the right path, we only missed the win. We played well, with possession and very clear openings. The result is a pity."