Messi returned from injury to help La Liga champions Barca to a 2-1 victory against Inter at Camp Nou on Wednesday.
Discussing Messi's performance post-match, Valverde stressed that the Argentine can still change games even when he's not 100 per cent fit.
"It is the first game that he played in full, also a game with a significant physical burden on the opponent and the competition," Valverde told reporters.
"In any play he can help you even when he is tired. Messi has not done a pre-season like the others, so he has to catch up.
"In the end he made a fantastic play, but he was more tired than at the beginning."
Suarez silenced his critics with a brace – making it three goals in two games – as Barca rallied past Antonio Conte's Inter on home soil.
Lautaro Martinez had silenced the crowd with his second-minute opener, but Suarez restored parity approaching the hour mark before getting Barca's Group F campaign up and running following their goalless draw at Borussia Dortmund.
"Strikers live in the danger zone," Valverde said.
"They play in the most difficult area as they are always surrounded by defenders and need to solve the situations against the defenders they have onto them, so that is hard.
"Sometimes you cannot succeed, like one week ago, but then he scored once for La Liga and twice for Champions League. Luis has probed for a long time already what he is capable of, so he keeps doing so."
Barca have struggled to convince this season amid growing pressure on Valverde and the Spanish boss is aware how crucial the victory was.
"Of course this is an important win as it was a very important game, given how tight the group table was after the first match-day and also for the upcoming games," he said.
"From the very first minute you all saw how important this game was for both teams given the intensity we both showed. I hope this comeback will help us for the upcoming fixtures."