Southampton's Erwin Koeman declared his team ended Vitesse's resistance when Graziano Pelle struck early in Arnhem.
Graziano Pelle's fourth-minute strike effectively put Southampton's UEFA Europa League qualifying tie against Vitesse to bed, according to assistant coach Erwin Koeman.
The Italian striker drove the ball into the bottom corner of Vitesse's net early on Thursday to give Southampton a 4-0 aggregate lead in the third-round qualifier.
While Vitesse finished the match with 16 shots to Southampton's seven, Koeman argued that Pelle's strike deflated the Dutch hosts in Arnhem, as the Premier League club went on to win 2-0 in the second leg to wrap up a 5-0 aggregate result.
"After four minutes, when Graziano made a fantastic goal, it was a lot easier for us," Koeman, who was standing in for his injured brother Ronald, told Southampton's website.
"That meant that they had to make five goals, and that's normally impossible - and it was impossible.
"I know the fans over here and last week in Southampton they were great, like our fans. Today they hoped there would be a miracle but, after four minutes and a great goal by Graziano, it was over."
Sadio Mane ensured Southampton of the win on the night with an 89th-minute goal.
Southampton will begin their Premier League campaign away to Newcastle United on Sunday.