Goals from Santi Cazorla and Aaron Ramsey at the Emirates Stadium on Saturday enabled Arsenal to open up clear daylight between themselves and a congested chasing pack.
Having seen his side often fall short in matches against title-chasing opponents in recent seasons, Wenger was delighted with the result and performance.
"It was important to convince people we can win these big games," the Frenchman said.
"It was an important win for the team, for the club, and I believe that nobody could dispute that we deserved to win."
Asked about Arsenal's chances of claiming a first league crown since 2004, Wenger replied: "I'm always confident but of course there is a long way to go.
"It's unpredictable because who would say Chelsea would lose at Newcastle after Tuesday night (when they defeated Arsenal 2-0 in the League Cup).
"We have been consistent since January 1, 2013, with the same group of players. We have 25 points from 10 games - it is a very respectable return."
Arsenal's victory over Liverpool came without the injured Jack Wilshere, while Kieran Gibbs was forced off in the second half.
It remains to be seen whether either player will be fit for Wednesday's potentially pivotal UEFA Champions League tie at Borussia Dortmund.
Wenger added: "Jack has an inflamed ankle. Will he be available for Wednesday? I do not know. We will have to wait until Monday to see.
"Gibbs has a calf problem. I don't know exactly how bad it is."
