Despite being the second best during the opening stages of the game, the Toffees had their tails up kind courtesy of a superb strike from James Rodriguez on the 30th minute mark.
The visitors kept knocking and eventually got their equalizer when goalkeeper Jordan Pickford allowed Belgium international Youri Tielemans’ shot slip through his grasp inside 67 minutes.
Dominic Calvert-Lewin, who has not scored a goal in the league since against Burnley on December 5, had the chance to snatch the maximum points for the hosts but failed to do so as both teams shared the spoils.
"It was a tough game. I thought we defended more than we attacked, we did quite well and it's a good point,” Ancelotti told BT Sports after the game.
"We didn't have the control that we wanted when they equalized, the game was more in their control but the point was fair.
"It wasn't that we defended too deep, it was the fact we didn't quite have the quality after they equalised.
He added: "I said two weeks ago this is an unpredictable league, unbelievable. There are good games and hard games - we played against Sheffield United, who are at the bottom, and had problems. It's a really exciting Premier League."
Next up for Ancelotti and Everton is a home game against Newcastle United in the Premier League on Saturday.
