The result leaves Arsenal six points clear at the top of the Premier League.
Arteta said afterwards: "We know that the margins are very small. I think we have two different halves.
"The first one, where we have a lot of domination, created big situations with players almost onside the six-yard box to pick a player up, and we didn't find the right pass to score the goal. And the second half was a bit more of a struggle.
"This game needs some magic moments, and at Anfield, (Dominik) Szoboszlai did it, and they won the game, and today it didn't happen, but you cannot win it, you cannot lose it.
"We have some moments where we have the right positional advantages to really hurt them, and then when we got into these areas, we lacked quality to pick the players.
"We've come from a very demanding schedule. The last six games that we've played in this Christmas period, and we've come out of that in a really strong position."
On the controversy around Arsenal attacker Gabriel Martinelli trying to push injured Liverpool defender Conor Bradley off the pitch, Arteta added: "Probably he doesn't know because knowing Gabi, there is zero intention.
"I don't know what happened to Conor, but hopefully it's not bad, but obviously, there is no intention from Gabi to do anything bad to him."