Sam Gallagher, Calum Chambers, Billy Sharp and Steven Davis were all on target as the new manager took the opportunity to view a number of his squad with 11 changes at the break
Koeman succeeded Mauricio Pochettino at St Mary's Stadium last month and has been hampered by the departure of several star names, with Luke Shaw and Adam Lallana following Rickie Lambert in sealing moves away from the club.
However, Southampton were able to field one of their new recruits, Dusan Tadic, as they kicked off their pre-season preparations with a routine win in the Netherlands.
Youngsters Sam Gallagher and Calum Chambers were on target in a first half dominated by the Premier League team.
Koeman then made 11 changes at the break, with Tadic among those introduced, and saw his side pull further clear with goals from Billy Sharp and Steven Davis.
Defender Dejan Lovren, who has expressed a desire to join Lambert and Lallana at Liverpool, was absent from Southampton's team, while another new arrival, Graziano Pelle, also played no part after only joining up with his new team-mates on Monday evening.
Against modest opposition, it took Southampton just 11 minutes to make a breakthrough as a deflected strike from McQueen deflected off a defender and looped over EHC's goalkeeper.
Further chances went begging before Chambers headed home an inswinging McQueen cross to double his side's lead in the 44th minute.
Southampton then added two goals in three minutes shortly after the hour mark, Sharp converting a penalty and Davis firing home a rebound after a header from Gallagher had come back off a post.
Koeman's side will now return to their training camp in Belgium before facing KSK Hasselt on Thursday.
Swindon Town, Bournemouth and Brighton and Hove Albion will also pose pre-season opposition for Southampton, who round off their preparations with a home game against Bayer Leverkusen on August 9, a week before the new Premier League campaign begins.