Victories for Atletico Madrid and Barcelona this afternoon meant that Ancelotti's team had to win at the Anoeta Stadium to remain three points adrift of their Liga rivals.
"I appreciate the whole game because we played very well, very intelligently. I'm very happy," Ancelotti said to Marca after the game.
"It wasn't easy but I have a team that likes to fight. I'm proud to coach this team."
The Spanish giants travel to Germany on Tuesday for the second leg of their Champions League quarter-final tie with Borussia Dortmund, before resuming domestic duties by hosting Almeria at the Bernabeu next weekend.