The Argentine, who spent last season on loan at PSG from Inter before signing permanently, has endured a difficult season impacted by injury.
"I'm glad Mauro scored three goals tonight," Pochettino said. "Anytime he's on the pitch, he has the opportunity to score.
"He's coming back from injury, I'm very happy with what he did."
Icardi has battled the likes of Neymar, Kylian Mbappe, Moise Kean and Angel Di Maria for a regular spot when fit.
Pochettino would not be drawn on whether Wednesday's hat-trick would help the Argentine's cause in a bid to start in Saturday's Ligue 1 clash with Metz.
"We will see Saturday who will start," Pochettino said.
"It is always difficult for a player to suffer from muscle damage and to be held back by health problems. Even more so in a season of difficult circumstances like this."
Icardi's goals take his season tally to 11 in all competitions, having made 21 appearances.
"I felt confident," Icardi said. "I'd already scored against Saint-Etienne and I was very confident that I could come back after a tough injury hit year.
"I'm slowly getting back to form and scoring goals is always important for strikers."