De Gea let a tame first-half effort from Said Benrahma slip into the net as United suffered their second straight league defeat. They remain fourth and a point above Liverpool, who have played a game more.
Ten Hag said he hoped the goalkeeper will extend his stay at the club. His contract is set to expire in the summer.
"He has the most clean sheets in the league so we would not be here in this position without him," Ten Hag told reporters. "He fully has my belief. No concerns with him.
"It happens but as a team you have to deal with it, show character, be resilient and bounce back. We want him to stay and extend his contract."
Asked if Liverpool's six-match winning run had affected his side, Ten Hag said: "It's not about Liverpool, it's about us because if you look to the table we have everything in our hands.
"Nothing changes. We could have made it easier if we had won, but we need three wins in four games. Everything is in our hands. We have to believe."
