I mean, access to the playoffs was on the line, so yeah. A very, very big deal.
One can also argue for simply making a chippie field goal and finishing undefeated in 1979.
The loss to Baylor in '83 proved very costly. It was the difference in back-to-back undefeated seasons. With a winning streak that long, who knows what the end of the season in '84 looks like. More likely, IMO, that Washington agrees to play us in the Holiday Bowl instead of opting for the bigger money payout. But we won the natty anyway, just not with a resounding exclamation point due to Michigan's 6-5 record.
Washington in '96--again, would've likely resulted in a big bowl. Not sure if we'd have gotten a chance at the title though.
Those last two are all in the benefit of hindsight with what would eventually be on the line...only 1979 really compares in terms of something worthy having being right there for the taking in the moment.
I've got no other examples. The big bowls had already passed on us when we lost to Hawaii in 2001, so that's out.