"IT WAS AWESOME!"

The legendary NFL coach was still giddy on Sunday when we spotted him out in NYC -- telling TMZ Sports he was stoked he got to share that special moment with the world

"It was pretty awesome. Pretty surreal to be honest with you," Cowher said ... "Very surprised!"

Cowher was doing his thing on the CBS pregame show before the Ravens vs. Titans game, when Pro Football Hall of Fame president David Baker suddenly walked in and interrupted to inform Bill he's getting a gold jacket!

The moment was amazing -- Bill got super emotional and thanked everyone who helped him along the way ... all while his cohosts cheered their faces off!

The very next day, Baker surprised Jimmy Johnson on the set of the NFL On Fox pregame show and delivered the same news to the ex-Cowboys coach. His former player, Troy Aikman, was so moved, he choked back tears.

Another emotional moment. Great stuff!