The Uruguay international was taken off seven minutes from time with his side two goals to the good and well on course for an eighth win in nine outings.
Suarez was visibly upset with Valverde's decision, though, even refusing to shake his manager's hand as he departed the Camp Nou field.
Asked about the incident after the match, Valverde attempted to play down the matter when telling reporters: "Suarez is ambitious and no-one likes to be substituted.
"Everybody wants to be an undisputed starter every time. I do not see any problem. It was the third game he has played in six days, and he is getting chances, which is the main thing for a striker."
Suarez, not included in Uruguay's latest squad due to an injury concern to his knee, has three goals in nine outings for Barcelona this term.