Asked about his decision, Lichtsteiner replied: "Ronaldo? I don't regret leaving because that was what I wanted. I wanted a new challenge.
"Anyone would be happy to join Juventus, but now it's Arsenal who count."
The 34-year-old went on to wish his former side luck in the Champions League this season as they look to take their dominance of Italian football onto the European stage.
He said: "I hope Juventus win the Champions League, they deserve it after losing two finals."
Lichsteiner began Arsenal's first game of the season on the bench but was forced to make his Premier League debut at left-back following an injury to Ainsley Maitland-Niles midway through the first half.
Arsenal went on to lose the match 2-0 but Lichtsteiner still believes his new side will do well this season and are capable of bouncing back from the disappointing result.
Speaking after the match, Lichtsteiner said: "We will work very hard to come back. We improved in the game.
"We're Arsenal and we like to play football, even against Manchester City.
"It's very difficult, but like I said, he's [Unai Emery] had us working very hard.
"We wanted to win! But we will look forward and work hard for next time."
Arsenal's tricky start to the season continues with a trip to Chelsea this weekend.