"The scenario looked a lot like that," said Kosar, whose attempt to tie the score died when Earnest Byner fumbled the ball near Denver's goal line with 1:05 to play, securing the Broncos' 38-33 victory in the AFC Championship.
Denver, which took a safety in the closing seconds, advanced to the Super Bowl on Jan. 31 against Washington.
One year earlier, Bronco quarterback John Elway drove his team 98 yards to tie the conference title game 20-20 with 37 seconds to play, and Denver won, 23-20, in overtime at Cleveland.
Kosar's drive, had it been successful, would have covered 75 yards and tied the score 38-38.
"I wasn't looking at it in terms of matching that performance," Kosar said. "I was just looking at it in terms of the scoreboard.
"But I have to be honest with you, I thought about last year's drive because I knew we needed a touchdown at that point. There was no doubt in my mind that we had the ability to do it."
Byner's fumble spoiled what had been a comeback from a 21-3 halftime deficit that Cleveland had essentially handed to the Broncos.
The Broncos' first touchdown came after Freddie Gilbert intercepted a deflected Kosar pass at the Cleveland 18-yard line. Denver made it 14-0 on a 60-yard drive after Kevin Mack's fumble was recovered by Steve Wilson, and the Broncos' third touchdown was aided by Chris Rockins' 15-yard penalty for hitting Elway late on a scramble.
"Without the turnovers, they wouldn't have been in the game," Byner said. "They wouldn't have even been close."
The halftime score wasn't bad enough to dull the Browns' spirit, however.
"We knew we hurt ourselves in the first half because of all the mistakes," Kosar said. "But we didn't get this far by quitting. We just went out after them."
The Browns eventually tied the score, 31-31, on Kosar's 4-yard pass to Webster Slaughter with just under 11 minutes go play, and a teary-eyed Coach Marty Schottenheimer said later that the Browns would be heard from again next year.
"I've been involved in this game as a player and a coach for a long time," Schottenheimer said. "I've never been more proud of a group of men than the group I was associated with today. We dug a big hole for ourselves but we kept working. Unfortunately for us it wasn't quite enough."