It was Arsenal's biggest win over Chelsea since a 3-0 victory in Wenger's first meeting with them in April 1997 and the 66-year-old said he was now even more eager for success than when he arrived.
"I'm hungrier because I know I have not got 20 more years in front of me," smiled Wenger, whose team rose to third place in the Premier League table.
"I also feel a responsibility. You can't be 20 years somewhere and not care. I'm more conscious about what Arsenal is all about and I feel the weight of keeping people happy, and making people happy."
Wenger felt his side's football had been "nearly perfect" in the first half and said their overall display was "one of our best performances of recent years".
Chelsea have held something of a hoodoo over Arsenal in recent times.
Sanchez's 11th-minute goal, after a mistake by Gary Cahill, was the first league goal Arsenal had scored against Chelsea since January 2013.
Chelsea dealt Wenger a humbling 6-0 defeat in his 1,000th game at the Arsenal helm in March 2014 and he said Saturday's win could mark an important mental breakthrough.
"We had to deal with some inconvenient facts before the game. They were we couldn't beat Chelsea for years," said the Frenchman, whose side host Basel in the Champions League on Wednesday.
"To get that out of the system was also at stake today. I think what was important for me was the psychological hurdle standing in our way. We mustn't make too much of it, but we can't ignore it.
"We couldn't say to the players they'd always done well against Chelsea, because that wasn't true. I told them to focus on the quality of football, to have belief, and today they did that."
The one black spot for Wenger was a first-half knee injury sustained by Francis Coquelin.
The French midfielder, who was replaced by Granit Xhaka, left the stadium with his leg in a brace and will undergo tests in the coming days.
- 'Find the right solution' -
Chelsea have gone three league games without victory and while beaten manager Antonio Conte refused to single out individuals for blame, he had strong words of criticism for his team.
"Now we are a great team only on paper, not on the pitch," said the Italian.
"To be a great team, I prefer to be a great team not only on paper but also on the pitch. The pitch is the truth. The pitch speaks."
Chelsea switched to a back three early in the second half -- Conte's preferred defensive configuration with Juventus and Italy -- and he said he would urgently address their problems at the back.
"I have to solve the situation," he said.
"Two at the back, three at the back, four at the back, I don't care. I just have to solve this.
"I must find the right solution for this team because, in every game, we are conceding two goals minimum."
Both managers were asked to evaluate their team's title prospects.
"The title? I think we must work a lot to find some continuity," said Conte, whose team trail leaders Manchester City by eight points.
"I think that, now, the most important thing is to work and not think about other situations."
Wenger was more optimistic.
"Between winning a big game and the Premier League, there's a long way to go," he said.
"At the moment Man City look a long way in front, but if we maintain the quality of our performances and stay consistent, we might have a chance."