The La Liga champions looked rampant for the first 30 minutes of Saturday's game as Alexis Sanchez broke the deadlock after seven minutes and Barca then spurned numerous other opportunities before Dani Parejo equalised against the run of play at Camp Nou.
The visitors went ahead early in the second half through Pablo Piatti, only for Lionel Messi to level from the penalty spot.
Paco Alcacer netted the winner after good play by Sofiane Feghouli in the 59th minute, ending Barca's 31-match unbeaten run at home in the league.
And Martino was at a loss as to how and why his team switched off after the first half an hour.
He said: "Looking at the first 30 minutes, it can't be explained how the game changed after that. We were another team in the second half.
"I said before the game that you pay dearly for every mistake from now on, and we made several mistakes.
"(I said at half-time) That this isn't over, we shouldn't give up, that we might be behind after this round (the first half), but we'll fight.
"Now we have to rise to the occasion. This should hurt, but it shouldn't have an influence on the future.
"When you can finish off the opponent, you should do it, you shouldn't give them chances. We did and Valencia took them."
Barca midfielder Sergio Busquets echoed Martino's view that the home side had enough chances to defeat Valencia.
"It has been a long time since we lost here,” he added. "It's a slip at a bad moment. It's a pity, we had our chances.
"We suffered in defence."
