Bale scored his 100th Real Madrid goal in the derby win.
Solari said, "He came back into the dressing room smiling, he was happy with his goal.
"He rounded off a game that was intense and every day he seems to be better."
He added: “We're all part of the team and the key thing is the players, who are the ones who train, show the physical commitment and heart in every game. The players deserve 95% of the credit for the win.
"The remaining bit is down to the rest of us - the medical team, directors, fans… Real Madrid always fight to the end and we have to keep going. We have to keep our feet on the ground and continue working hard."