Serbia, who reached their first major soccer tournament as an independent nation, produced their most effervescent qualifying performance on Saturday and won Europe's Group Seven ahead of 2006 finalists France, who are assured of a play-off spot.
"We've just raised the bar for ourselves and expectations will be high but it needs to be said that the Romanians did not deserve such a heavy defeat," Stankovic told reporters.
"We were under a lot of pressure to finish the job in front of 50,000 home fans and we were flying after the second goal.
Striker Nikola Zigic opened the floodgates in the first half before Marko Pantelic, Zdravko Kuzmanovic and a late Milan Jovanovic brace completed the rout.
"It was important to take something into the dressing room at half-time and the opening goal allowed us to control the match in the second half," Zigic said.
"We are now going to enjoy ourselves and celebrate because the impressive run that got us here also put us under a lot of pressure to qualify automatically.
"Now that we have booked a place in South Africa, I am sure that we will play the best we can and not let our fans down in the finals."
Thousands of Serbia fans celebrated in central Belgrade into the early morning hours of Sunday, with players parading in an open-top bus.
The Serbians are away to Lithuania in their final group match on Wednesday and coach Radomir Antic said his team would not be content to just go through the motions.
"We will be a bit more relaxed but we want to win to improve our world ranking and be top seeds in the draw for the Euro 2012 qualifiers," he said.
