Bradley produced a man-of-the-match display as Liverpool cruised to a 4-1 win over Chelsea, a result that restored their five-point lead at the top of the Premier League over Manchester City and Arsenal.
The right-back has shone in the absence of Trent Alexander-Arnold in recent weeks and his continued his fine form against the Blues, scoring his first goal for the club and assisting Diogo Jota and Dominik Szoboszlai.
Bradley was brought off to a standing ovation in the second-half, as Christopher Nkunku then pulled one back for Chelsea before Luis Diaz put the match to bed for good.
Klopp was full of praise for the 20-year-old after the match, as he discussed how Bradley has made an impression behind the scenes over the past few years.
"He has the biggest advocates in the club," Klopp told TNT Sports.
"It's three years already that Pep Lijnders is in my ear. 'Put both hands and my feet in the fire, he will be [ready]'.
"Vitor Matos [development coach] and Pep are very integral in this department. They really are advocates for the club. My job is the easiest one, I just have to put them on the pitch."
He added: "What a wonderful kid he is. Outstanding finish, the whole game, the contribution, the involvement.
"It's a job to play against [Raheem] Sterling, that's not easy. I'm really happy for him. He's a very serious young man and that was pretty special I have to say."
On an eventful night at Anfield, Darwin Nunez was typically chaotic, remarkably hitting the woodwork on four occasions with the 11 shots he had at goal across the 90 minutes.
The post kept out his penalty before half-time, as Liverpool missed out on the chance to take a 3-0 lead into the break, but Klopp was still impressed with the "outstanding" forward.
"He was really disappointed with himself about missing the penalty but he is a handful," the Liverpool boss said.
"It was really hard for him. Then he headed against the crossbar. He sets up a goal even after the massive disappointment. That's the most important thing. He is in outstanding shape, still a bit unlucky so it's all fine."