The coach praised the Welshman's first appearance for the club, although he remained unsatisfied with the draw against Villarreal
The €100 million arrival was handed his first start for his new club and immediately repaid Ancelotti's faith with a goal when he slid in Daniel Carvajal's cross.
Although Giovani dos Santos ensured Villarreal took a share of the spoils with a late goal, Ancelotti was pleased to see Bale hit the ground running alongside Cristiano Ronaldo.
"I was happy he got to score his first goal for Madrid. It's great for him. He played in a game that was tough for everyone," the Italian noted to reporters after the match.
"He showed a good attitude on the pitch. It was the first time they [Bale and Ronaldo] played together. We swapped their positions from time to time because they kept cutting infield. But it's nothing particular."
Asier Illarramendi was also handed his full debut, and Ancelotti was pleased to see the midfielder get some playing time under his belt after a lack of action so far in 2013-14.
"I think they [Bale and Illarramendi] were good, but suffered a bit at first. I did not give them 90 minutes because that is not possible in the first game. But they had a good debut," he said.
Diego Lopez was retained between the posts at the expense of Iker Casillas and single-handedly kept Madrid in the game with some superb stops - although Ancelotti believes his side should have won the game irrespective of the Spaniard's exploits.
"Diego was responsive, intelligent and played very well," he said. "I do not know if he saved us from defeat but maybe with more care we could have won the match, because at 2-1 it was easier for us.
"With a little more attention, especially in midfield, we would have won the game."
Saturday's draw leaves the Santiago Bernabeu outfit fourth in La Liga on 10 points, two behind leaders Barcelona and Atletico Madrid.