Spurs saw their hopes of qualifying for the Champions League suffer a setback as they were beaten 1-0 by their local rivals at White Hart Lane.
Sandro and his teammates are now seven points adrift of the top four places in the table with eight games left to play.
"We showed passion, won every ball and gave 100%," the Brazilian told the club's official website. "We gave everything, we pushed, but it wasn't enough.
"I know this means a lot to everyone. It's the biggest game and we lost. It's difficult. We have to stay together and I know the fans are with us."
Tottenham return to action on Thursday when they will try to overturn a 3-1 first-leg deficit against Benfica in the last 16 of the Europa League.