Leganes had made things interesting in Camp Nou when Martin Braithwaite cancelled out Ousmane Dembele's opener in the second half.
The goal forced Valverde to introduce Lionel Messi from the bench, and he inspired Barca to go on and win – playing a role in Suarez's goal before then rounding things off late on.
Suarez's goal was contentious from Leganes' perspective, as Ivan Cuellar saved Messi's strike and then the Uruguayan netted from close range, appearing to collide with the goalkeeper at the same time.
Replays showed that, although there was contact, it was minimal and the goal stood even after a VAR review, angering Leganes.
Valverde thinks sense prevailed, however.
"I thought it was a goal," Valverde told Movistar. "What can I say, everyone sees it from their point of view, but if the referee has given it, it will be a goal.
"With VAR, the controversy is not over. It's a clear goal. Suarez does not touch the goalkeeper, they have reviewed it.
"There will always be controversy, mistakes will follow and you have to accept the error. That [errors] will not end with VAR, nor if it was a robot refereeing."
Carles Alena impressed in midfield before being withdrawn for Messi shortly after the Leganes equaliser.
The crowd reacted negatively to Alena's withdrawal, but Valverde made the change for a specific reason.
Speaking in his post-match news conference, Valverde said: "Alena played a great match, but we thought it was a good idea to make changes at 1-1.
"[Ivan] Rakitic and Messi are used to playing together and we have opted for a turn, but that does not mean it [Alena's performance] was not good.
"The other day the full game, Alena did not play and today he did. We have to give everyone games because they are all important."