The Brazil international stole the show at the International Champions Cup on Saturday, scoring a brace in a 2-1 Barca win at MetLife Stadium.
Neymar is heavily linked with a move to Paris Saint-Germain, but showed no signs of that being a distraction as he impressed in the first half.
Valverde, who enjoyed a win in his first game in charge, knows how important the 25-year-old is to his side.
"Barcelona will not do without Neymar," he told a news conference.
"We want him to be with us and we know the impact he has in our game. It's clear."
While Barca dominated the first half, Juve improved in the second and Giorgio Chiellini's header saw them pull a goal back.
But Valverde was relatively pleased with what he saw from his team in their first pre-season outing.
"We wanted to try to take the initiative, try to be together, always intending to dominate the game knowing the difficulty of the opponent," he said.
"We are also in a phase where we have to add minutes and take confidence. This victory is very positive."
Barca are next in action with a clash against Manchester United on Wednesday.