The Gunners did give up a lot of chances in the game, but had their own moments in front of the Reds' net.
Lacazette had an excellent opportunity to make it 2-2 in the second half, but spurned his chance and hit it straight at Liverpool keeper Alisson.
But Arteta was not too critical of the Frenchman post-game.
"Obviously he had the best chance in the game to make it 2-2, and then again put us in a really strong position, but he had a great game," Arteta said post-game.
"He put in another incredible performance and I'm pleased with him. I want to see my players upset and angry when we lose a game.
"It is a really tough place to come, they are a really good side. We stayed in the game for almost the whole match.
"Having took the lead, we should have held that situation a bit better. We conceded the goal too early.
"We competed well knowing the difficult moments you will have when you come to Anfield; when we had the clear chances to make it 2-2 we didn't take them.
"They want to win and this is what they are like, the mindset of the team. They go to any ground and want to win. They really believed we could come here and do it and for large periods of the game we were there."