Dominik Szoboszlai's free-kick proved the matchwinner for Liverpool on the day.
Arteta said afterwards: "We didn't do our gameplan to frustrate them; we did it to win it. I think we elevated the game and the dominance to a point that they had to raise it. They did, especially from the 60-78th minute, when then you could see that there were no margins in the game.
"When that happens, the game is going to be decided in two ways. One, with an individual error, and two, with a magic moment. Szoboszlai created a moment that was incredible, that has won the game, and that was the difference, nothing else."
On Liverpool's fight-back after halftime, Arteta says it was to be expected.
"Because this is Anfield and at some point, it's going to change. You cannot dominate Anfield for 95 minutes and it changed in various ways, especially because we didn't make the right decision when our keeper got the ball in their hands, we started to rush it, the turnovers, we didn't manage them so well so we could never glide as a team. They are going to create those moments without really creating any situations of danger."
On William Saliba's injury and Cristhian Mosquera's performance, Arteta added: "He twisted his ankle during the warm-up, and he came in and he said he believed that he could carry on and play, but straight away in the first two actions.
"I could see that he couldn't cope, and we had to get him out unfortunately. But thank God we had Mosquera, which we put in for the first time in the Premier League. His debut, not expecting it at Anfield, and I think he was really, really good."