Last season's Rookie of the Year Doncic made a career-high eight three-pointers and had 35 points, eight rebounds and seven assists as the Mavs defeated the Portland Trail Blazers 120-112 at American Airlines Center on Friday.
Anthony had 22 points for the Blazers, who slipped to an 18-25 record and sit 2.5 games back of the playoff positions in the Western Conference.
When the 10-time All-Star was informed Doncic had referred to him as a "walking bucket", he returned the compliment.
Anthony continued: "As far as Luka goes, he's gonna be in this league for a long time.
"He's a young player and he's gonna get better and better. For years to come we're gonna to be watching a special player.
"I hope you guys out here in Dallas really appreciate what you have in front of you right now."
Anthony, who in November joined the Blazers after nine months without a team having been waived by the Chicago Bulls following his trade from the Houston Rockets, became the 18th player to reach 26,000 career points when he scored a free throw in the first quarter in Dallas.
"This is a situation where I've always continued to believe in myself and I think with that being the case I'm able to still go out there and perform the way I want to be able to perform and enjoy the game again," he said.
"I think people understand the situation I was in, but most important I think people understand the type of person I am. When you have that organic natural energy, people pick up on those vibes."
Portland lost CJ McCollum to a left ankle sprain in the second quarter and he did not return to the game. It is unclear if he will be fit to face the Oklahoma City Thunder on Saturday.
"Usually, the second day is the worst," McCollum said. "So we'll see how it feels [on Saturday]. Get some treatment, try to compress it and see how it feels."