The London club had not won any silverware for nine years until they beat Hull City to lift the FA Cup at Wembley in May.
Arsenal had looked genuine contenders to win the Premier League in the 2013-14 campaign, but lost their way and ended up finishing in fourth place.
Wenger made a statement of intent by bringing in Alexis Sanchez in a big-money move from Barcelona and has since signed Calum Chambers, Matthieu Debuchy and David Ospina.
And the Frenchman, who signed a new three-year contract in May, is bullish over his side's chances of being crowned champions of England for the first time since 2004.
He said: "I never made any excuses (for Arsenal's lack of trophies). I took it on my shoulders.
"But I knew the situation. I accepted the challenge when I signed my contract, knowing what would happen. I thought, personally, it was the most sensitive and important period of my career here.
"It was exciting, to manage to keep the club at the top level with less resources. Did we do well or not? The only thing I can say is we were consistent at the level. But we lacked the quality to really win it. Now we have that.
"Even last season we were very close to the Premier League, just seven points behind Manchester City. Our belief has grown.
“I expect a lot but I can talk and talk - at the end it’s the performance on the pitch that will show how much chance we have to win the Premier League.
"We have more confidence than at the beginning of last season. Our opponents have also strengthened. It’s everybody's ambition to win the league - but only one will win it."
Wenger refused to reveal whether he would have walked away from Emirates Stadium if Arsenal would have failed to beat Hull as he plots more success for the London club.
"I always said the same thing to you, that I wanted to think I had done well for the club," he added.
"My motivation was never at stake and I never questioned that. Did I want to go somewhere else? Never. I always wanted to stay.
"But I needed to feel, as well, that I had done a good job and of course the fact we couldn't win was going on in my mind. It was important for me to feel I have done a decent job."
