The 18-year-old, who was in disbelief following the historic win, also praised the home support and hailing them as the "12th man".
BBC Sport quotes Watt as saying: "It will take a couple of hours for [the result to sink it]. I just saw Victor Valdes and put it in the corner. I couldn't believe it, it's probably the best moment of my life.
"We'll look back and say, 'wow, we've beaten Barcelona in the Champions League' - it doesn't get better than that.
"The crowd were like a 12th man, I've never heard anything like it, the place was rocking."
The victory consolidates Celtic's position in second place in Group G, leaving them two points behind leaders Barca.