"I thought it was great, I enjoyed it immensely, I was surprised to start the game," Beckham said. "Of course, I'm still working on my fitness but I felt good, better than I thought I would in the game. [My aim] is to play as many games as possible and work on my fitness and just be part of AC Milan. I feel very lucky."
Ancelotti said Beckham earned the start with his work in the days leading up to Sunday's game.
"I played him from the start because during training in the week he worked hard and earned it," the Milan coach said. "It wasn't a gift and he showed it by playing well. We agreed he would start but kept it quiet so as to protect him from all the attention. He was ready to play in this team because he is intelligent and he understands how this team plays. We were able to keep our balance with him in midfield. He played a simple and very disciplined game. I think in the next match he can give even more quality.
Beckham played on the right side in a three-man midfield alongside Andrea Pirlo and Clarence Seedorf.
Celebrating the first anniversary of his Milan debut, Brazilian teenager Alexandre Pato scored two goals sandwiched between goals by Montenegro striker Mirko Vucinic.
The tie left Milan still nine points behind city rival Inter after 18 games.
The purpose of Beckham's offseason loan from the Los Angeles Galaxy is to keep him fit to stay in the England national team plans of Coach Fabio Capello, though Ancelotti insisted Beckham was at Milan to help the Rossoneri, not prolong his international career.
"If he [Capello] wants a report," Ancelotti added, "I would only have positive things to say because I have trained many players but it is not easy to find one with the professionalism Beckham is showing."
England's next game is a friendly against Spain on Feb. 11. If he plays, Beckham will equal Bobby Moore's of 108 caps for a field player.
Beckham insisted that he will return to the Galaxy in March.
"That's what's been agreed and that's what I'll stick to," he said.