"The vote of no confidence is something that a member is trying to get off the ground," added Bartomeu.
"He is within his right to do so, but I don't think there are the extraordinary conditions for such a motion.
"There is no sporting crisis because we have started the project with Ernesto Valverde very well. Economically the club is in rude health with a record turnover."
Valverde has suffered plenty at the hands of Messi in his coaching career at Espanyol, Valencia and Athletic Bilbao before being given the reigns at the Camp Nou.
And he admitted it is far easier being on the same side as the five-time World Player of the Year after his first taste of Champions League action as Barca boss.
"I have suffered many times playing against Messi and now I have the luck to have him on my side," said Valverde.
"We know that when he gets the ball anything can happen. Today he opened up the game in one moment where no one saw the gap and he found it."
Valverde has already experienced the ups and downs of his new role just over a month into the season as his reign started with a 5-1 thrashing by Madrid in the Spanish Super Cup before a run of four straight victories.
"In football when you lose it seems like you are never going to win and when you win that you will always win," Valverde added, warning against complacency.
"Inside the club we need to maintain calm because we know how difficult every game is."