Messi was rested at Estadio de la Ceramica and initially Barca looked to be coping fine without him as they went 2-0 up thanks to Philippe Coutinho and Malcom – who also set up the opener.
But Samuel Chukwueze pulled one back and Karl Toko Ekambi punished poor positioning from Marc-Andre ter Stegen to equalise, before Vicente Iborra and Carlos Bacca had seemingly secured a famous win for Villarreal.
Substitute Messi found the top-left corner with a fierce free-kick in the 90th minute, however, and Luis Suarez's rasping drive deep into stoppage time secured a share of the spoils.
It was put to Valverde that Barca are perhaps too reliant on Messi, and the coach acknowledged there was an element of truth to that assessment.
"Of course there is a Messi dependence, of course it exists, he is the best in the world," Valverde told reporters.
"But we must know that when he isn't playing, we must play the same way, like in the first half.
"There was no Messi dependence [in the first half] and the team was fine and [should have been] able to win the match."
Although it proved to be a difficult outing for Barca, Valverde believes such a tussle will serve them well for the remainder of their title race and Champions League campaign.
"This game has helped us a lot, especially for the games that are to come," he added. "It makes people realise that the league is complicated, the teams are good and they have a spirit to fight.
"They [Villarreal] are a good team and they have troubled us. We must improve so that the opponents do not take us lightly, because we will play against teams that play for the league and the Champions League, and against those teams you cannot do that."
The draw leaves Barca eight points clear of second-placed Atletico Madrid, who visit Camp Nou on Saturday.