Unai Emery believes Arsenal are closer to Liverpool than last season despite another chastening experience at Anfield.
Having lost 5-1 last December, the Gunners were beaten 3-1 this time but were under pressure for the vast majority of the game and faced 25 shots.
It took Liverpool until just before half-time to make the breakthrough, Joel Matip heading in. Mohamed Salah's double early in the second half threatened to make it another battering but Arsenal rallied and substitute Lucas Torreira scored a consolation.
Emery said: "It was not all we wanted to do in the match because we wanted to keep the ball more, but their pressing was very strong. The second half the key was the penalty. I think (it was) very soft, I think usually it is not enough.
"But we continued our way, we opened more and they gave us more space to keep the ball. In the transition they are very strong and they scored the third goal.
"It was the moment we needed to show something different – not frustration, not (heads) going down. I think we showed character, also the impact with Lucas Torreira, with (Alexandre) Lacazatte and Mhiki (Henrikh Mkhitarayan) was good.
"Some players today made one step ahead, like (Joe) Willock, I think also it was a good match for (Nicolas) Pepe and Matteo (Guendouzi). (Dani) Ceballos struggled more than last week but it is one experience more for him.
"We need to be optimistic. I think we reduced the distance with Liverpool. At the moment it's not enough but I think we can be, in some issues, positive."
Emery admitted full-back Nacho Monreal, who played the full game, could leave the club before the closure of the European transfer window having been heavily linked with a move to Real Sociedad.
"With Nacho, one possibility is open and we are going to speak about that," said the Gunners boss.
On the continued absence from the squad of Mesut Ozil, he added: "Today they are here the players who we think they were the best physically and to play today."
Liverpool are now the only Premier League side with a 100 per cent record this season and extended their winning run to 12 league matches.
Jurgen Klopp felt this performance represented a step up, saying: "I was really happy with a lot of parts of the game. I think everything we did well in the first four games we did tonight longer, more precise and better attuned.
"And I loved the desire, the passion, the power, the energy we put into this game that made us really uncomfortable to play against. We have a lot to improve but it was a big step tonight and I'm really happy."
