Pochettino is currently under pressure at Spurs having lost two games in five days, conceding ten goals in the process.
The 7-2 Champions League defeat at the hands of Bayern Munich was compounded by the 3-0 loss to Brighton on Sunday, and Wenger had spoken out about the difficulties of being at one club for an extended period.
He told beIN SPORTS: “I think he [Pochettino] has done very well, which everybody acknowledges.
“I experienced that at Arsenal. We were twenty consecutive years in the top four but in the end it was not enough anymore.
“Today if you get into the Champions League people are very happy.
“That’s happened to Pochettino, when you have been somewhere for four or five years, you have to show people you can give more – he is at that stage.”
Wenger, who managed Arsenal from 1996 until 2018, won three Premier League titles with the Gunners, but none after 2004.
When asked if he sees any parallels with his own time at north London, including the move into a new stadium, Wenger added: “Well yes, I would say that they’re a bit destabilised as well.
“When I played them two or three years ago they looked like a young hungry team who had found a good strength and a good core, with people who were growing together inside the club, and players from outside who are vital like [Christian] Eriksen.
“Today, you don’t feel exactly the same chemistry, and a player like Eriksen is a bit sidelined because he looks like he doesn’t want to commit his future at the club.
“Modern life is down to small margins, and at the moment this small margins are not in their favour.”
“Will they get that back? Because if you look at Tottenham in the Premier League they lost 13 games last year but they’ve done extremely well in the Champions League and came close to winning it.
“It’s down to small margins.
“Your real quality is always where you finish in the table. So the real trend is there.”
Tottenham are currently ninth in the Premier League after eight fixtures, having won only three of their games.