"I don't think you can have an outstanding team performance when the individuals don't work together," Klopp told the BBC. "The start was brilliant, we were really going for them. We were outstanding, it was a top game.
"We could have scored and should have scored more goals. You cannot score five, six goals against Chelsea if you are not outstanding."
Liverpool moved five points clear atop the Premier League to set up a potential thriller on Sunday against third-placed Arsenal.
Liverpool have 51 points after 22 games, while Manchester City and Arsenal both have 46, with City having a game in hand.
"It's so clear they were much better than us. We lost every single duel. Every time we recovered the ball after one or two touches we lost it," Chelsea manager Mauricio Pochettino told TNT Sports.
Twenty-year-old Bradley's goal was his first for Liverpool but was not a complete surprise as the Northern Ireland youngster has been excellent at right back since replacing injured Trent Alexander-Arnold. He earned a rousing standing ovation and huge hug from Klopp when he was substituted.
"Incredible. Wonderful. He's flying at the moment," Klopp said. "Rightly so. He's working hard and is a good footballer. He's helped us so much it's incredible. Quite a few people said we need a right back in the summer but we were very positive about Conor.
"All the injuries we have, we can't string these results together if these boys don't show up." Klopp added.
Darwin Nunez was relentless in attack, but hit the post with a first-half penalty, and had numerous other near-misses. The Uruguayan became the first player since 2003-04 to hit the woodwork four times in a Premier League match.
"He was really disappointed with himself about missing the penalty but he is a handful," Klopp told the BBC. "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."
Former England and Newcastle striker Alan Shearer had a similar sentiment, telling the BBC's Match of the Day, "Darwin Nunez does not stop getting in behind. I like his perseverance and that is why he will definitely score goals."
