Bale started on the right wing at El Madrigal and was largely a peripheral figure until he slid home Real's equaliser on 39 minutes after Cani had given Villarreal the lead.
The Wales international was substituted on 61 minutes after missing most of pre-season through injury and Ancelotti was satisfied with his record buy's impact.
"I think he's happy to score his first goal for Real Madrid," Ancelotti told a press conference.
"He played in a difficult match and he played well, showing his good attitude. It was a hard match for everyone."
Asier Illarramendi also made his debut in the game and Ancelotti added of the two new boys: "They played well. Their performances were good.
"I didn't play them for the full 90 minutes because in the first match it isn't a good idea, so after an hour I took them off."
Midway through the first half, Bale swapped wings with Cristiano Ronaldo, who put Real in front before former Tottenham attacker Giovani Dos Santos earned Villarreal a point.
Ancelotti said: "It was the first time they've played together and they will swap positions now and then because their movement is in towards goal from the wings.
"But they might change wings sometimes, it's nothing out of the ordinary."
The draw was the first time Real had dropped points in La Liga this season, but Ancelotti was happy to come away with a point.
"It was a difficult match," said the Real coach. "I don't think that was the worst that we have played.
"The different rhythm of the two teams was obvious, but that's to be expected because after the international matches it's difficult. The rhythm and preparation are different, it's not just a physical problem but also mental.
"The team's reaction after the first goal was good. We scored two goals and if we had paid a little bit more attention we could have won but it's a fair result because Villarreal played well. They are a good team."