Arteta's second-placed side moved within two points of Liverpool with a dynamic display at the Emirates Stadium on Sunday.
The Gunners took the lead through Bukayo Saka's early strike, then recovered from conceding Gabriel Magalhaes's own goal on the stroke of half-time.
Gabriel Martinelli put Arsenal back in front after Liverpool goalkeeper Alisson Becker missed his attempted clearance on the edge of the area.
Liverpool defender Virgil van Dijk accepted the blame for failing to clear the ball himself but it was a costly mix-up with Alisson, who also allowed Leandro Trossard's shot to go through his legs in stoppage time as Arsenal wrapped up the points.
The significance of Arsenal's first win over Liverpool this season at the third attempt was not lost on Arteta, who celebrated Trossard's goal with a jubilant sprint down the touchline.
After blowing an eight-point lead in the title race last season, allowing Manchester City to steal the crown, Arsenal are desperate to finally win the Premier League for the first time since 2004.
And Arteta hopes the mature way they recovered from conceding the equaliser against Liverpool showed they now have the attributes required of potential champions.
"We are there, that's for sure. We want to continue to be there," he said.
"We've been really consistent all season, if not you aren't where we are today.
"We take it game by game. We have learned that from last season. Let's try to make that happen."
After blowing the lead in their 1-1 draw at Liverpool in December, then missing a host of chances in an FA Cup third round defeat by Jurgen Klopp's team in January, Arsenal were intent on proving a point to the Anfield outfit.
"It was an extraordinary game. An incredible performance from the players and our people. That's the best atmosphere I've seen all season. We demanded that," Arteta said.
"They put their heart and soul in every single ball. I cannot be any prouder because I know how hard it is to beat this team, how much you have to suffer and how much you have to process to do what we did on the ball."
'Very chaotic'
Arteta said Arsenal's commitment to a high-pressing, attacking philosophy had left Liverpool breathless as the pressure mounted in the second half.
"Control is not really a word I like. I like dominance and not allowing teams to breathe more than control," he said.
"In which part of the pitch that happens is the most important thing for me but, yes, we can be very chaotic in open spaces and can create a lot of issues playing in different ways. That is another weapon that we have."
Liverpool's first defeat in three games since Klopp announced his intention to quit at the end of the season was a major blow to their title bid.
Beaten in domestic action for the first time since September, Liverpool looked unusually vulnerable at the back.
"Today, everything went against us. We got a red card. Some situations could have been different. But it's done, I don't care about it anymore," Klopp said.
Last crowned champions in 2020, Liverpool will be overtaken by Manchester City if Pep Guardiola's side win their two games in hand, starting at Brentford on Monday.
"At the final whistle I didn't think for a second about the number of games left for City," Klopp said.
"We have to play to our potential and deal with difficulties around the games and play with our soul on the pitch and we will see where it ends up.
"I am not nervous now because of two games in hand for City. We expect them always to win their games. Nothing really changes. We would have loved to win here but we were not good enough.
"Today, nobody celebrates as champions and nobody is relegated. We have time to create our own destiny."
