Koeman urges Netherlands players not to drop performance level after Romania win
Goals from Cody Gakpo and substitute Donyell Malen, who scored twice, sealed victory from a game in which the Dutch dominated from the start and might have added more goals.
It was a far cry from the dismal display in their last fixture, a 3-2 defeat by Austria in their final group match a week ago.
"It is sometimes difficult to say why you play bad in one game and then can reach a high level the next match," Koeman told reporters.
"We were sharp from the beginning today and that made the difference. Maybe one critical point is that it took too long to score the second goal."
The Dutch face either a rematch with Austria or a clash with Turkey in the quarter-finals on Saturday and Koeman believes their attack from both wings and the excellent display in the midfield by Xavi Simons was the key to victory.
If they are to reach the final in Berlin on July 14, they cannot let their performance level drop again.
"The result is always the most important thing, but we are Dutch and in Holland we have to play well and offensively. We know that," Koeman said of fan expectations on the team.
"The whole performance today was outstanding and that is what we need to do to continue in this tournament. This is the level, if we go down from this we won’t reach the final."
Koeman was in the Dutch side the only time they lifted the Euros trophy, in West Germany in 1988. He said it was difficult to compare teams from different eras as the game had changed.
"We have great talent in this team but of course you need to win something, then people can start to compare with 1988," he added. "But it is more difficult now, football has changed, it is more physical, you need to be fast and technically good.
"England, Portugal, everybody has their own problems to continue in this tournament."
Koeman will sweat over injuries for midfielder Jerdy Schouten and Steven Bergwijn, who were both substituted against Romania after complaining of niggles.