Barca were stunned 3-2 by Atletico in the Supercopa semi-final, conceding two late goals to sensationally lose on Thursday.
Goals from Lionel Messi and Antoine Griezmann cancelled out Koke's 46th-minute opener until Barca shipped twice in the final nine minutes as Atletico earned a showdown with Real Madrid.
The result plunged Valverde's future further into doubt but star forward Suarez defended the 55-year-old.
"[Valverde] is not to blame, the mistakes were ours and we can't make them," Suarez said post-match.
"I do not know if they are defeats that help us grow, [but] this defeat shows that there are things to correct.
"It shows us that there are mistakes that cannot be committed because we were in control of the game and we have allowed them to hit us on the counter-attack."
Griezmann was frustrated afterwards as the Barca forward lamented the side's errors against LaLiga rivals Atletico.
"I think we lost due to our own errors and they had the legs at the end," Griezmann said. "It cost us and we have to work hard in order to continue.
"We all made errors. I played a bad pass and then their goal arrived. They are errors which can cost you a Champions League or a league title."