The France worldwide has been heavily tipped to leave the Nou Camp for Arsenal or PSG after a hard debut season in Catalonia last term.
And, speaking after the match, Valverde lauded the 21-year-old and expressed a belief that Dembele would get even better over time.
'We need a bit of shooting practice, but we are happy because in spite of everything, we have beaten a great rival, ' Valverde told the club's official website.
The Brazilian was in no doubt as to how important a part both Ousmane Dembele and Marc-Andre ter Stegen played in the match. The Blaugrana looked disjointed for large spells of the first-half, but fortuitously levelled proceedings through Gerard Pique when the defender latched on to a rebound off Lionel Messi's freekick.
'The most complicated thing when you play against a super team is that you have to compete, that means making it hard for the opponent with all your weapons.
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Midfielder Sergio Busquets also joined the pleas for Dembele to stay: "I hope he continues here, of course - that he continues and that this season goes better for him than the last, when he had bad luck with injuries".
"We knew that the circumstances of this match were different". He skilfully evaded his markers to get into good positions and strung together some silky passes that his teammates let go begging.
"It was a really hard game because we conceded very early and we had to fight back".
"It is good to win because it boosts you in what you're doing and allows you to start the season in a positive way".