The Lakers had a one-point lead with two minutes left in a game against New Orleans on Tuesday.
Clark made a layup, helping the Lakers secure a 111-106 win.
"It's great for a great player like that to have trust in me because, you know, he could have easily shot it," Clark said of Bryant. "He's so great, he can make shots over the double team any day. It just feels good."
Clark's clutch play impressed Bryant.
"He's playing extremely well," Bryant said. "He can make plays, he can shoot the three, he has a good mid-range game, he can finish at the rim. He can also make plays for everybody else."
Clark has risen from being buried on the depth chart to becoming a starter for the Lakers, ahead of Pau Gasol, a four-time All-Star.
On Tuesday, Clark finished with 20 points and 12 rebounds. He shot eight of 11 from the field and made a career-high four three-pointers.
Against Houston on Jan. 8, Clark played what was then a season-high 20 minutes. The following game, he had a career-high 22 points and 13 rebounds against San Antonio.
Clark said his recent success had worked wonders for his confidence.
"I feel more comfortable about making plays," he said. "If I turn the ball over I'm not looking over at the bench because I know Coach [Mike D'antoni] has trust in me and he's just not snatching me if I make a mistake. That feels great."
It wasn't always that way.
In the past, Clark sometimes might appear at the end of games, when the outcome was already decided. He felt as though he were playing under a microscope during those moments.
"Just coming off the bench you got so much pressure on you," he said. "You haven't been playing and you get in with one minute and 30 seconds left.
"If you get in with one minute and 30 seconds, one turnover, that's like you want to kill yourself because you want to play so good and show the coaches that you can play. When you get in and you make a bad turnover, you cant sleep at night."
During that time, Bryant helped keep Clark's spirits up.
"I mean, just telling him to stay with it and telling him that his number was going to be called," Bryant recalled telling Clark. "To his credit, he worked every single day and never got discouraged."
Clark said that he considers Tuesday's performance his best game ever in his NBA career.
"I'm just trying to do whatever coach tells me to do, you know, guard the best players, rebound, and whatever I can do to help the team win," he said.
During the game, Staples Center honored the Lakers' newest starter by playing the song 'Duke of Earl' in front of its sold-out crowd.
Clark soaked it up.
"Man, it's cool," Clark said.