Schweinsteiger set up both goals for striker Mario Gomez on Wednesday as Germany beat Holland 2-1 in Group B to leave Dutch hopes of progressing to the knock-out phase hanging by a thread after two defeats.
The Oranje must now beat Portugal in Kharkiv, Ukraine, on Sunday and hope Germany win against Denmark in Lviv, Ukraine, the same day to be sure of reaching the last eight.
Schweinsteiger embraced Holland captain Mark van Bommel in the centre circle after the match in Kharkiv, Ukraine, and the German star told his former Bayern Munich team-mate that Germany will do their best to beat the Danes.
"All I did was tell him that we'll give our all against Denmark and then it is in their hands to win against the Portuguese," revealed Schweinsteiger.
"There is no need to tell you he was very disappointed, but I am confident the Dutch will beat the Portuguese."
Having now beaten both Portugal and World Cup finalists Holland in the pool dubbed the "Group of Death", Germany have justified their status as pre-tournament favourites for Euro 2012.
Schweinsteiger split the Dutch defence twice in the first-half to set up Gomez, but the 27-year-old midfielder insists solid defence is the key at Euro 2012.
"The teams who stand solid at the back will get far at this tournament, that is the key to success here," said Schweinsteiger.
"You really have to work hard defensively and check what the opponents are doing yourself.
"We have a lot of individualists up front, who have free rein to a certain degree, but defensive order is of full importance.
"Even if you play an attacking style as a principal philosophy, you still have to have the over-all picture in mind.
"If you look at Spain or Barcelona, the Spanish defenders are always looking at what the opposition forwards are up to and that is the perfect approach to winning games."
Victory or even a draw will see Germany finish as Group B winners and give them a quarter-final on June 22 in Gdansk, where Germany are based.
"That would be important, but first of all it is more important to win against Denmark, play good football, work very hard defensively and use the spaces they grant us," said Schweinsteiger.
"It would be great not to travel, I think everyone had major problems getting back from Kharkiv to Gdansk."
The German team's flight back from Kharkiv was delayed by 30 minutes in the early hours of Thursday morning and the team did not reach their hotel until 0400 local time (0200GMT).
Reporters accompanying the team had a three and a half hour delay and arrived at Gdansk airport at 0630am local time.