The Seminoles led 51-40 with 13:06 remaining. The Wolfpack, however, responded with five 3-pointers and took advantage of various FSU possession miscues to take a lead and hold it for a 78-71 victory.
The Seminoles haven't played in the NCAA Tournament since 1998.
"N.C. State did a real good job of keeping their poise," FSU forward Michael Joiner said.
"And they're really confident. It's almost like they've been in that situation before. I think that's something we have to take from that game ... just to be poised, be disciplined and stay together."
Both the NCAA and NIT field will be announced tonight. Either way, FSU will be on the road.
The Tallahassee-Leon County Civic Center is booked Tuesday and Wednesday, and the arena is also unavailable Friday through March 22 because of the NCAA women's basketball tournament.
Joiner said an invite to the NIT also represents a big step for FSU's program.
"It's definitely a positive step, just from the simple fact we haven't been in postseason since I've been here," said Joiner, who has played four years. "If we have to go to the NIT just to make it to the NCAA next year, it's definitely a great path.
"It's a nice feeling knowing we have a chance to be selected in the NCAA Tournament, but if not, the NIT tournament will still be a great feeling, just to be playing beyond this weekend."