The Gunners had fallen behind to a David Ngog opener, but salvaged a share of the spoils thanks to a last minute Pepe Reina own goal.
Both sides finished the contest with 10-men at Anfield, but Wenger was delighted with his side's never-say-die attitude.
“We had a lot of possession,” Wenger told Sky Sports post-match.
“Liverpool did well and did create many chances, we have to be complimentary, but we kept going [which] shows that we’re not giving up. It is a good result at Liverpool.”
A big talking point in the game came in the final minute of the first-half when Liverpool debutant Joe Cole was sent-off for a late challenge on Arsenal's Laurent Koscielny. However, Wenger admitted he didn’t have a great view of the incident.
“I saw [Laurent] Koscielny had the ball but I didn’t see the tackle” he commented.
The Arsenal manager also gave a debut to Marouane Chamakh, and the Moroccan striker made the challenge on Reina which resulted in the own goal. And the French tactician admitted he was happy with him and other new signing Koscielny's performances.
“[Mourane] Chamakh scored and Koscielny had an outstanding game, for me he was impressive," Wenger added.
After watching Ngog’s 46th minute strike fly past goalkeeper Manuel Almunia at his near post, Wenger refused to lay blame on his goalkeeper and instead praised the Liverpool forward for his strike.
Yet after signing a new contract at the start of the weekend, Wenger expressed his delight to have committed his future to the club.
“I am where I love to be, I love Arsenal and want to do well for the club,” he added.
“They trust me and give me freedom to work. I think by showing that kind of commitment at my age it shows that I will certainly stay at this club.”
And the Frenchman was confident his side can improve on last season’s third place finish.
“Our ambition is to do better, that means second or first,” he continued.
“I believe we can do it. We were not far away last year and the competition is open and very interesting.”
However, Wenger refused to comment on speculation linking the Gunners with move for a new gloveman, with both Manchester City's Shay Given and Fulham's Mark Schwarzer rumored to be high on the manager's shortlist.
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