The 29-year old striker stepped out for the Azzurri for the first time in Monday night's Euro2016 qualifier with Malta and marked his debut with a match-winning goal in the 23rd minute in Ta'Qali.
Pelle, who joined the Saints from Feyenoord in the summer, continued his brilliant club form for his country and St Mary's Stadium boss Koeman was delighted for his star recruit.
"I am happy he scored the decisive goal for the Italian national team," Koeman told reporters at a pre-match press conference," Koeman said ahead of Southampton's Premier League clash with Sunderland.
"I hope he can continue in this vain with the shirt of our club as well.
"His qualities have never been in question, he is doing great things and I think he can repeat what he did in Holland [with Feyenoord]."
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