The Blues could have leapfrogged Liverpool into top spot with victory at Goodison Park before the leaders kicked off at Tottenham Hotspur later in the day.
But instead Chelsea saw their eight-match winning run end as they failed to score for the first time since October.
And with Liverpool winning 6-3 in an extraordinary encounter in north London, it meant Chelsea ended the day in second place -- four points behind the Reds and having played a game more than the table-toppers.
Maresca -- speaking before Liverpool's victory was confirmed -- said: "I am absolutely happy. I just said to the players I am more happy today than I was after the Brentford game (which they won 2-1 last weekend).
"The reason why was I was quite worried about this game: tricky game, tricky stadium, tricky team."
He added: "Defensively they are top, they are one of the five best teams in Europe in terms of clean sheets so you struggle to create chances against them.
"It was not an easy game and you have to learn how to play different games. Football is not only just how good you play on the ball, it is how you defend and how you deal with that."
This was Everton's first match since the Friedkin Group (TFG) completed their takeover of the Liverpool club, with new executive chairman Marc Watts among the Goodison crowd on Sunday.
This was struggling Everton's second successive goalless draw following last week's 0-0 at Arsenal but Toffees boss Sean Dyche, out of contract at the end of the season, knows it is wins alone that will impress the club's US-based owners.
Everton have won just three of their 16 league matches so far this season, with the Toffees four points above the relegation zone.
"It wasn't my only goal (to send TFG home with a point) to do that but it is a nice add-on," said Dyche.
"We've had a good meeting with them, they seem really good, really serious people.
"People talk about my own position -- win games, they have made it clear. They are supportive of my role, what I've done here and what I hope we do. We have got to win games, though. I'm not naive."
