The Catalans took the lead through Alexis Sanchez but goals from Dani Parejo, Pablo Piatti and Paco Alcacer ended a run of 25 straight league wins at Camp Nou for Barca, which earned a consolation through a Lionel Messi penalty shortly before Jordi Alba was sent off.
With Atleti and Madrid both playing Sunday, Barca is on the verge of relinquishing its La Liga lead and Busquets didn't conceal his disappointment at handing an advantage to his side's title-chasing rivals.
"It had been a long time since we had lost here," the 25-year-old midfielder told reporters after the game. "It's an untimely slip-up. Valencia made the most of their weapons and we were unable to do more. They're in better shape under their new coach and they have really good players.
"We started well. We played well for the first hour and created a lot of scoring chances. Then they played their hand and we didn't play well. It's unfortunate. You have a hard time of it when you concede three goals, of course."
Barcelona's reversal has given Madrid, which travels to face Athletic Bilbao on Sunday, and Atleti, which hosts Real Sociedad, the opportunity to push the Blaugrana down into third as the Spanish title race continues to twist and turn.
Los Blancos will be without Gareth Bale for the encounter at San Mames, while Diego Simeone's men have had their ranks bolstered by loaning Diego from Wolsfburg.