The pressure has been building on Setien after a run of two wins in five matches, leaving the reigning La Liga champions four points adrift of leaders Real Madrid.
The 61-year-old was only appointed as Valverde's successor in January, however, and Bartomeu is pleased with the progress Barca have made during his short tenure.
"He will continue, evidently," Bartomeu told RAC1."I'm happy with the progress of the team; in the last two games you have seen progress. First we try to win the league and then the Champions League.
"I don't regret the change with Valverde, we needed an impulse; Setien has brought in fresh air, an impulse.
"The squad is being renewed, the current players are doing well. Sergio Busquets, [Gerard] Pique, Luis Suarez, [Lionel] Messi, they are doing well; the mix of youngsters - Pedri, [Francisco] Trincao - and veterans is very good."
Barca are back in action on Wednesday with a home match against city rivals Espanyol, who sit bottom of the table.