The Italian has accused the Chile international of deliberately conning the referee to earn the spot-kick which allowed Xavi to score a second away goal
The Chilean was brought down by Salvatore Sirigu late on with the scores level at 1-1, allowing Xavi to notch a second away goal before Blaise Matuidi's last-gasp equaliser.
Although replays showed there was contact between the players, Ancelotti insists the referee made an incorrect call, but claimed he is used to the former Udinese winger attempting to earn fouls.
"Alexis looked for the goalkeeper, it was not a penalty," he told Canal + after the match. "It was a gift from the referee.
"We have experience with Alexis, in the friendly in August he also dived. We know him. He likes to dive. It is nothing new."
The Italian went on to praise his side's resolve on the night, insisting they proved they can compete at Barcelona's level ahead of the return leg at Camp Nou.
"It was a good game. We played well in the first few minutes but it got complicated. We used a lot of energy to level the score," he continued.
"We have opportunities for the return game. It is still open, even if it will not be easy. We showed that we can compete against Barca. We will have to score twice there. We did it tonight, let's do it the same way in the second leg."
Director of football Leonardo voiced his own admiration for the team's display, and paid particular tribute to the tactics deployed by Ancelotti on the night.
"We are very, very proud. We conceded when we were at our best in the game, and to come back in the game against Barcelona is not easy.
"Carlo was amazing today. He studied Barcelona hard, and it is true that if you look at the game, we had a nearly perfect strategy. We had one goal when we were the best. But if you leave a few millimeters to [Lionel] Messi, this is what happens.
"I believe that after all we've been through in the past few months, today is truly a wonderful thing, because it is not easy to build a team. We are very proud of our game, our behaviour, our approach to the game.
"It is true that it is very difficult there [at Camp Nou]. But you never know. With this spirit, we'll try everything."