Pepe has impressed in his second season at the Gunners, scoring 14 goals and notching five assists in all competitions so far this term.
The 25-year-old has mainly been played on the right wing by Mikel Arteta this campaign, emerging as a regular starter under the Gunners boss.
The winger scored two goals to help Arsenal secure the win which has solidified their place in the top-half of the league.
Pepe opened the scoring after 35 minutes, volleying in Keiran Tierney’s cross after a neat move down the left from the visitors.
Palace did equalise through Christian Benteke’s diving header, with the game seemingly headed for a draw.
But Gabriel Martinelli converted fellow substitute Martin Odegaard’s cross from close range before Pepe claimed his brace by cutting in from the right and slotting past Palace keeper Vicente Guaita.
Ljungberg spent two years as a coach at Arsenal, serving as interim manager when Unai Emery was sacked before joining Arteta’s staff as an assistant.
And he was full of praise for Pepe, insisting that his goalscoring instinct is something that was seen in training frequently.
“I like him. He’s awkward to play against. Has good speed. One against one he’s very, very good,” Ljungberg told BT Sport.
“This [his goal] is what I saw in training every day and it’s what you want to see in every game.
“Of course there’s other parts of his game he needs to learn but if you can put him in these situations he’s lethal all the time.”
Despite that praise though, the former Sweden international believes Pepe still has some parts of his game that need to improve.
“He came from a league where he could cheat a little bit his defensive work, wait a little bit, he countered, he’s one against one and scored a lot of goals,” Ljungberg said.
“Maybe at Arsenal he needs to do a lot of other stuff. He needs to work more like a unit, do more defending. And I think that’s what he learning at the moment.”