Davis made one of his two foul shot attempts, increasing the Lakers' lead to two, instead of three.
With 7.2 seconds left, Davis was called for a foul against Kleber on a 3-point attempt. Kleber went to the foul line and made all three of his free throws to cut the Lakers' lead to one.
"I already came in and told them the last play was my fault," Davis said after Friday's game. The eight-time All-Star has taken blame for several Lakers games this season.
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The Lakers fell to 34-37 on the season. A win would have boosted the team's playoff chances because two teams ahead of them — the Warriors and Timberwolves — both lost.
"It's tough all the way across the board," Davis, who scored 26 points, said.
Mavs superstar Luka Doncic sat out of the game with an injury. The win pushed the Mavs into the sixth spot in the conference.
Wenyen Gabriel, who had nine points and 11 rebounds off the bench, said he still believes in Davis.
"I mean, AD is our leader," Gabriel said. "He's our best player right now, and that just shows that taking accountability as being the best player.
"That's something that's important for the continuity as a team and having trust in each other, and obviously we trust AD. That was just a moment. It's obviously not just on AD, but him taking accountability for that is something that is important instead of pointing fingers in terms of chemistry going forward."
The Lakers play the Orlando Magic Sunday at Crypto.com Arena.
The Lakers had a slow start to the season and are fighting to get into the postseason. The team will need Davis to play at a high level, especially as LeBron James continues to deal with a foot injury.
Los Angeles played well after the All-Star break, winning six out of eight games. But the team has lost three out of its last four games.
"We're missing our opportunities, for sure. It's frustrating," Davis said.