The 18-year-old was making his competition debut against the Spanish giants on the club's 125th anniversary, and slotted past Victor Valdes for a goal that will seal his place in Celtic folklore.
The striker seemed dumbstruck after the game, stating that it 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," Watt told Sky Sports.
"This is probably the best moment of my life. I'll look back on this when I'm older and think, we've just beaten Barcelona in the Champions League. There's nothing better is there?"
The striker stated that he had never heard anything like the fans at Celtic Park, insisting that they are 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. The place was rocking from start to finish," he said. "The fans were the best in the world, they just kept singing and singing."
Victor Wanyama got the other goal for the hosts, nodding home in the first half to open the scoring, and said that it was an unreal and unbelievable night for the team.
"This is unbelievable," he stated. "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 our first goal so it was very important, and that gave us energy to go on."
Wanyama also revealed that Neil Lennon's side had been training on set-pieces ahead of the encounter, and insists that the club can make the knockout stages if it just keep playing as it knows it can.
"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 added.
"We just have to keep going. If we keep on going and doing the same we're going to keep getting results and we'll be [in the knockout stages]."
Fraser Forster, meanwhile, praised the squad for their ability to adapt to the injuries they are currently suffering, and for ultimately getting the job done.
He said: "We've got a fantastic squad of players and whoever comes in will do tremendously for us. We really showed in the Nou Camp what we can do and we just couldn't see it through.
"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."
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