The Italian coach insists the Liga title race will go right to the wire this season and refused to blame the referee following Sunday's 4-3 defeat to Barcelona
Messi struck for the first time just before halftime but Cristiano Ronaldo restored Real's lead with a controversial penalty on 55 minutes.
But Messi delivered from the spot twice in 20 minutes as Sergio Ramos was sent off, putting Barca to within a point of top spot in La Liga as he broke Alfredo Di Stefano's long-standing record for goals scored in the Clasico.
Ramos and Ronaldo were quick to criticize referee Alberto Undiano after the match, but Ancelotti was more concerned with the errors in his side's play.
"It's difficult for me to comment on the referee's decisions," he told reporters after the match.
"It's true that Messi scored three goals but any mistakes against a player of his quality will always hurt you.
"We have nine matches left. It will be all intense. Every game will be decisive."
Atletico Madrid is now top of La Liga following a win over Betis, while Barcelona is just a point behind the capital clubs, and Ancelotti believes this season's title race will go right to the wire.
"The league race is still open. We need an immediate reaction," he added.
"I've said it many times – the league will be decided in the last match. We have to continue fighting. We need to react.
"I haven't spoken to the players about the match yet. We committed small mistakes and that's why we lost.
"The team is ready to get up and move on. We have to be satisfied with how we played.
"We have improved a lot, the team has showed its quality and proved it in this match. It was a good game but we now have to forget about it quickly. Our next match is important."