Mikel Arteta's team, last season's runners-up who have won five of their last seven matches but not tasted victory in a league game at Anfield since 2012, have 40 points from 18 games. Liverpool are second on 39 points, ahead of Aston Villa on goal difference.
"An unbelievable game of football, one of the most intense I've witnessed in 20 years in this league," Arteta told the BBC. "For many moments we were on top, in the last 20 minutes we wanted it more, but a draw is a fair result."
In 10 of the last 14 seasons, the leaders on Christmas Day have gone on to win the title. Champions Manchester City are fifth, but have played one fewer game.
Arteta was happy with his side's performances but felt that Liverpool were able to cause them problems by creating chaos.
"We were determined to attack and cause them problems. They are a team who cause chaos, they are so vertical and direct. They are the best in the world at doing that," he said.
"It was an unbelievable game of football with two teams that raised the bar to another level."
Arsenal will spend Christmas Day top for the second successive season, although they may have been knocked off their perch before they play again on Thursday.
Liverpool and Aston Villa, who are one point behind, are both in action on Tuesday.
"I'm happy to be where we are. Tomorrow we have a beautiful dinner with our families, then back to work," Arteta said.
While Arsenal have won five of their last seven league games, Arteta said they still need to improve if they are to stay ahead in a tight title battle.
"Yeah of course there are certain things that we have to improve. Especially killing games," he said.
