A first-half brace from Mario Gomez put the Germans in the driver's seat, and even though Robin van Persie got one back in the 73rd minutes, it wasn't enough to prevent defeat.
This was the Oranje's second successive Euro 2012 loss, and one which left them in serious danger of being eliminated in the group stages. The 2010 World Cup finalists were one of the pre-tournament favourites, but have now lost to Denmark and Germany, making their next game against Portugal a must-win encounter.
In comments reported by UEFA.com, Sneijder, expecting to be one of the star performers in Poland and Ukraine, said: "It's mainly disbelief that I am feeling right now.
"Having said that, we know that our game needs to improve. We need to get our routines on the pitch back, the things we are used to, the courage to play. Maybe in that last game, because we know we have to win it, there'll be no other chance. It's all or nothing on Sunday [against Portugal], and perhaps we can bring our own football back in that game."
Winger Arjen Robben, who failed to make much of an impact and was subbed by coach Bert van Marwijk seven minutes before full-time, lamented the fact that the Dutch were now dependent on other results for progression into the knockout stages.
"For sure there's still a chance," said the Bayern Munich player.
"We need to think that if Germany fulfil their sporting duty [by putting out a full-strength team against Denmark], then it is still in our own hands if we beat Portugal by two goals. But we are reliant on them and that doesn't feel good."
Meanwhile, Rafael van der Vaart, whose introduction at half-time tilted the game somewhat in Netherlands' favour, admitted his side were second-best before the interval.
"It's quite a blow, of course," he said.
"You have to take your chances, then it gets easier, but they got two chances and scored two great goals. They were the better side, you have to acknowledge that. In the second half it was the other way around and maybe we deserved more, it just wasn't to be. They got tired somewhat, we got stronger and scored a magnificent goal."