The 20-year-old inspired Los Blancos to a 3-2 victory over Napoli in the Champions League on Tuesday evening, setting up Vinicius Junior for his side's first of the match, before scoring himself in the 34th minute following a brilliant run into the penalty box.
Bellingham has now scored eight times and registered three assists in nine appearances for the capital giants since arriving from Borussia Dortmund over the summer.
Ancelotti, who has coached many of the biggest talents in the world, has said that it is difficult to understand how the midfielder is achieving so much at a young age.
"I'm surprised that he's 20 years old because he seems to be 30 because of his character and personality. He is always focused on the game and knows what he has to do," the Real Madrid boss told reporters.
"It's rare in a 20-year-old boy. He has a lot of quality, physical strength, and ability. He surprises me like everyone else."
Ancelotti also paid tribute to his side for their "complete" performance against Napoli, who managed to level the scores at 2-2 from the penalty spot in the 54th minute.
Real Madrid secured all three points late on, though, courtesy of an own-goal from the Italian team's goalkeeper Alex Meret.
"We played a complete and serious match. We played very well in the first half and after the goal, we did very well between the lines and created opportunities," he added.
"The dynamics of the match changed after the penalty and Naples pressed higher. We suffer for 10 or 15 minutes and then we take control and score at the end.
"The success of the first half has been because the positions of Bellingham, [Federico] Valverde, and Rodrygo created many doubts for Napoli in the game between the lines. The result is fair and I was expecting a Napoli with quality and dangerous players."
Ancelotti also explained why he once again selected Eduardo Camavinga at left-back despite having both Fran Garcia and Ferland Mendy available for selection.
"I didn't want to change the team that did very well in Girona. It was an important game and we did it well. I put only Rodrygo, who had rested. Camavinga gives us a lot. In the first half, we have done well because of its characteristics," he added.
Real Madrid will be aiming to make it four straight wins in all competitions when they continue their La Liga campaign at home to Osasuna on Saturday afternoon.