We came within a lucky shot and a now-defunct rule of winning in '87. (Clock would have stopped with 4 seconds left, our ball, down 1 under current rules.)
We ran into the best college team of probably the last 30 years in the '96 Final, and were within a couple buckets when Wallace fouled out on a phantom call with under 3 minutes to play.
We probably would have met Kentucky in the 2010 Final, if Arinze Onuaku had not blown out his knee right before the NCAA tournament. We still made the Regional Final without him.
In 2012, we were robbed of another Final Four in a horribly unfairly officiated game against Sullinger's Ohio State team, without Fab Melo, because of ESPN's bullteat sensationalizing of the Bernie Fine extortion case by that former ball boy. Melo, just to be clear, had already been suspended during the regular season for the very same thing they suspended him for a second time on the eve of the tournament.
So it's not like we haven't been close multiple other times. The last 2 trips to the Final Four, we were lucky to be there. Neither 2013 or 2016 were among our better teams. Both had clear flaws.