The 18-year-old, who made his debut in the competition against the Spanish giants on the club's 125th anniversary, slotted past Victor Valdes for a goal that will seal his place in Celtic folklore.
Watt seemed dumbstruck after the game, stating that the moment had not sunk in yet and would probably take a few hours to do so.
"I just saw Valdes, and I thought: 'Put it to the side of him', so I did," the teenager told Sky Sports.
|CELTIC 2-1 BARCELONA
|MATCH REPORT: Wanyama and Watt on target in historic Bhoys win despite Messi strike|
|TOP OF THE MATCH: Fraser Forster made several key saves to ensure an incredible result
The striker remarked that he had never heard anything like the fans at Celtic Park, hailing the support as the best in the world.
"They're the 12th man, obviously, and I said on the bench to the boys: 'I've never heard anything like it'," Watt enthused. "The place was rocking from start to finish. The fans were the best in the world, they just kept singing and singing."
Victor Wanyama, who opened the scoring for the hosts with a first-half header, delightedly declared: "This is unbelievable.
"Today we have just worked hard, we were good as a team, compact, and we got what we wanted and we are very happy.
"I can't describe it, I am just glad. It is just unreal to beat one of the best teams in the world. It's not easy, it was very tough, but we are very happy.
"It's always good when you're playing against this team to keep the ball and today we were very good and calm with the ball and that's what kept us in the game. We were good on the ball, we believed in ourselves. We got the first goal, so it was very important, and that gave us energy to go on."
Wanyama insists that Celtic can reach the knockout stages if they keep up their form.
"We have been working hard on set-pieces and we knew we were going to get one. I'm just happy. I'm happy for the team and we did well tonight," he continued.
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Goalkeeper Fraser Forster, meanwhile, praised the squad for their ability to adapt to the injuries that they are currently suffering and for ultimately getting the job done.
He declared: "We've got a fantastic squad of players and whoever comes in will do tremendously for us. We really showed in Camp Nou what we can do and we just couldn't see it through [losing 2-1].
"Even with a few injuries, we've got a fantastic squad, everyone was tremendous and everyone played their part. I think we deserved it in the end.
"We possibly [out-nerved them]. We defended really well. We had a good look at them a couple of weeks ago and we knew what we wanted to do. We didn't get it too wrong, and we managed to get the job done today."