The Saints enjoyed a fantastic return to the European stage on Thursday evening following a 12-year absence by comfortably defeating Vitesse Arnhem 3-0 at St Mary’s thanks to goals from Graziano Pelle, Dusan Tadic and Shane Long.
The only negative for Koeman was the injury suffered by midfielder Clasie, who saw a promising competitive debut cut short by a suspected hamstring problem midway through the second-half.
“Clasie did well,” the Southampton boss said. “He had a good help of (Victor) Wanyama, who was outstanding and that makes it more easy for Clasie.
“Pity he had some hamstring problems and we have to wait to know what happened.”
Clasie, a summer signing from Feyenoord, was replaced by fellow new recruit Juanmi and will have his injury assessed on Friday.
The Netherlands international does, however, appear a doubt for the second leg in Arnhem next Thursday – a match for which Koeman is not tempted to rest key men.
The game could also witness the long-awaited return of Jay Rodriguez after 16 months on the sidelines with a serious knee injury.
“It’s possible because he’s doing well, he’s not really like before but that’s normal because a long time out of competitive football,” Koeman added.
“He needs time and he gets that time and Sunday he will start against Espanyol (in Sunday’s friendly).”