The 19-year-old scored the opening goal and set up three more as the Dutch overturned a 1-0 playoff first leg deficit in style on Wednesday in front of their own fans to secure a place at next year's finals in Portugal.
"If you score the opening goal early in the match and set up two goals in the first half, it feels like you can fly," Sneijder told Dutch television on Thursday.
"Afterwards in the dressing room it was one big party, without tears but filled with emotions."
The Dutch squad refused to talk to the media after their win following reports, denied by the Dutch FA, that some of them had been partying after their 1-0 first leg defeat in Glasgow on Saturday.
But Sneijder was happy to break their silence on Thursday, adding: "We were a real gang that went for it, and we did exactly what we were aiming to do."
"In the dressing room it was more fanatical then ever and it was obvious we were eager to crush the Scots."
