The Dutch winger played the first 63 minutes of the Premier League victory at Old Trafford on Sunday before being replaced by matchwinner Dusan Tadic.
Elia is on loan for the remainder of the season from Bundesliga side Werder Bremen, where he made only 10 appearances in all competition this season prior to his St Mary's Stadium switch.
Despite Elia seemingly being surplus to requirements at the Weserstadion, Koeman was pleased with the Dutchman's first outing in a Southampton shirt.
"Yeah, you know he didn't play for a long time and he's not a player for 90 minutes," Koeman explained.
"He needs minutes to get the rhythm of the game. It was a good option for [the United clash], he's a fast player who can play one against one.
"I think he did well for an hour, little by little he will come back with his performance.
"I am sure it is a good signing for us."
Tadic's second-half strike moved Southampton up to third and keeps them firmly in the hunt for a UEFA Champions League spot.
When pressed on the possibility of qualifying for Europe next term, Koeman voiced his confidence that his side can maintain their lofty position.
"I'm not surprised we won [on Sunday] because I know the players and I know the organisation in the team," he added.
"I think if we keep the spirit and we know what we have to do then we can keep in front in the table."
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