An own goal from Ellyes Skhiri in the third minute and a Brian Brobbey strike four minutes later put the Dutch in complete control before halftime. A Jan Paul van Hecke header restored their two-goal lead after Tunisia had pulled one back, and the result confirmed the Netherlands as group winners heading into the last 32, where they face Morocco.
Koeman acknowledged the second-half drop in intensity with concern.
"I'm happy. I wanted first place in the group, and we finished that way," he said. "I'm just surprised by how easily we relaxed too much in the match.
"I think it had to do with the fact that we went 2-0 up very quickly. That can be a problem against a stronger opponent, and Morocco are an attacking team."
Tunisia's interim head coach Hervé Renard — appointed after the previous manager was sacked following a 5-1 opening defeat to Sweden — offered no excuses for a campaign in which his side conceded 12 goals in three matches without a single win.
"We were not at the level for this World Cup — this is clear, there is no discussion," Renard said. "It's a big tournament with very good teams, especially in this group. It was a very tough group. I already spoke to the players, I thanked them. But when you're in this type of psychological situation, it's not easy to tackle, especially when it's against a very strong team in an amazing stadium, and the crowd is packed with orange."
Tunisia's exit was confirmed before this match began after defeats to Sweden and Japan. They finish Group F bottom with no points and a goal difference of minus eleven.
The Netherlands go into the knockout stage unbeaten, having drawn 2-2 with Japan and beaten Sweden 5-1. Koeman's warning about complacency is timely — Morocco, their round of 32 opponents, arrive with significantly more firepower than Tunisia could muster.