Wes Welker's horse just got thiiiiiis close to winning his first pre-Kentucky Derby race at Churchill Downs ... finishing in 2nd ... for the 2nd year in a row.

As we previously reported, Welker re-entered his horse "Undrafted" to compete in the Twin Spires Turf Sprint Stakes ... the same pre-Kentucky Derby race he competed in last year.

But for the 2nd straight year, Undrafted couldn't quite reach the winner's circle ... getting edged out at the finish line ... to take 2nd place.

The good news ... 2nd place still gets paid -- and it all went down in front of Welker's old Patriots teammates including Tom Brady and Rob Gronkowski.

Hey, could be worse.