The Ivory Coast international has endured a slow start to his Gunners career after Arsenal signed Pepe in a £72m deal from Ligue 1 side Lille in the summer.
Pepe has scored one goal and has made three assists in 11 appearances in the Premier League so far this term.
The 24-year-old has racked up 742 minutes in the Premier League, starting eight games and coming off the bench three times.
The Arsenal record signing has been slightly more impressive in the Europa League following a return of two goals and two assists in four Uefa fixtures.
Henry famously took seven Premier League games to open his Arsenal account following his move to the north London side from Serie A giants Juventus in 1999.
The former Arsenal striker leaped to the defence of Pepe following his underwhelming start to the Premier League campaign.
“When you arrive like that, you’re always going to be talked about, and people are always going to target you,” Henry told Yahoo! Sport.
“He needs to make sure he doesn’t listen to that and go out and perform. People need to forget about the price tag.
“He didn’t ask to be bought for that amount of money himself. ‘It’s not always easy to arrive in a team, adapt to a new style of play.
“The Premier League, as we know, is not the same as the French League or any other league, by the way. So he needs to adapt to that. We need to give him time.
“People like to highlight the player but if the team were playing a bit better, maybe he would be playing a bit better.
“At the minute, it’s not a Pepe thing, it’s an Arsenal thing. Hopefully he and the team can get better so we can get in the top four again.”
Arsenal finished in sixth place in the Premier League table last term to miss out on a spot in the Champions League.
The Gunners signed six new players in the summer transfer window, including Pepe.
Arsenal lost 2-0 to Leicester City at the King Power Stadium last weekend following goals from Jamie Vardy and James Maddison.
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