Messi and Suarez both scored braces, while Ivan Rakitic, Ousmane Dembele and Jordi Alba were also on target as Barca routed Huesca 8-2 at Camp Nou on Sunday, FourFourTwo magazine reported.
Barca conceded first inside three minutes but the Spanish giant responded by netting three goals before half-time and head coach Valverde was pleased with the recovery, though he believes his side could have scored even more.
"We did a lot in attack, we scored eight goals, we played well and created a lot of chances. It's a good day, Huesca is a tough opponent," Valverde told reporters.
"They were good on the counter, with [Juan Camilo] Hernandez or [Alex] Gallar. The match in some parts was difficult but we were patient enough. We pushed them and we had enough resources to come back and score a lot of goals.
"In the first action of the match we conceded the goal, the second we also didn't expect because we had just scored the third. So at half-time we were a bit doubting ourselves. Then in the second half we won the match and we scored many goals because we played very well."
Barca moved top of the table, ahead of Real Madrid on goal difference but Valverde said, "The league just started. I don't give a lot of importance to being top of the table now because of goal difference. There are a lot of matchdays to come.
"Atletico [Madrid] and Valencia dropped some points but the league just started. Obviously we have to choose always to be on top."