The 18-year-old came off the bench to fire the SPL champions into a 2-0 lead as they made up for their heartache in Spain a fortnight ago when they lost the match in the 94th minute to take all three points with a 2-1 victory.
Certain to be regarded as one of the most famous results in the club's history, Watt admits it will take a while for the magnitude of Celtic's achievement – and the most important goal of his career – to fully sink in.
The ex-Airdrie player said: "This is definitely the best moment in my life. To score a goal against Barcelona which helped us beat them in the Champions League is incredible.
"It was a great feeling to climb off the bench and come on against them and play in such a special game.
"But to score a goal is something dreams are made of.
"I just managed to run on to Fraser Forster's kick-out and looked up and noticed Victor Valdes running out so I hit my shot as early as I could and it was brilliant to see it hit the back of the net."
Watt also admitted the atmosphere within Celtic Park was the best he has ever experienced.
He said: "I was saying to the boys on the bench I'd never seen anything like it because the place was rocking all night long.
"Our fans really are the best in the world and you can't beat Parkhead on European nights."
Team-mate Forster, who kept Neil Lennon's men in the match, added: "It's tremendous, I don't think words can begin to describe it.
"We had a good look two weeks ago and we knew what we wanted to do. Everyone was tremendous, everyone played their part.
"We defended really well and Tony came on and scored a great goal; his goals-to-games ratio is incredible."