The Spain international tore a knee ligament in the 3-0 triumph over Celta Vigo on Wednesday, cutting short what is expected to be his final year at the club.
According to reports, Valdes was the subject of interest from Monaco after he declared that he would leave when his current contract expires, but the injury has clouded his future.
Valdes also looks set to miss out on a place in Spain's FIFA World Cup squad and Martino had the 32-year-old at the forefront of his thoughts after Saturday's La Liga triumph.
The Barca coach said: "On behalf of everyone I want to give our support to Valdes. We dedicate this win to him.
"This team has become accustomed to bad news and their reaction is always to do better."
On the game itself, which saw the hosts finish with 10 men and was settled by Lionel Messi's second-half penalty, Martino confessed that it had been a tough test for his side.
He added: "Everything is still difficult. Derbies are not easy. You have to win, but it was a tricky one.
"There are seven finals remaining in the League. We are very aware of not making the mistakes we did in Valladolid."
Referee Carlos Clos Gomez endured a busy match as he controversially gave the champions a penalty for an apparent handball offence by Javi Lopez, before sending the hosts' keeper Kiko Casilla off for touching the ball with his hands outside of his area.
But Martino sympathised with the official.
"It was very difficult for the referee," he added. "He decided there was a hand for the penalty. I’m too far away to say.
"I find it regrettable that we don't talk more about football. I always learn something when we talk about football. It was the same in Argentina."
