The Celtic striker hit the headlines around Europe by netting the goal that clinched a famous 2-1 victory for Neil Lennon's side in the Champions League.
It also earned the 18-year-old a new deal, committing himself to the Parkhead club until 2016. However, Watt is already aiming for more highlights.
He said: "It's a goal but I have got a lot more to do in my career.
"Hopefully, I will continue to score important goals for Celtic and help the club be successful."
Watt also made it clear he hasn't allowed the moment to go to his head.
He said: "Everybody is stopping and talking to me and saying 'well done' for the Barcelona match. Ever since then I've been happy. I've just taken it in my stride.
"It has happened so I can't dwell on it. It will be a good memory for the rest of my life but I just need to get on with the season and maybe look back at the end.
"You don't want to go about bragging about it. It's obviously a big thing but other people have done it before and you.
"You don't want to be fazed by it and let it get in your head to make you start thinking that you are better than you are.
"I will never get ahead of myself and I just need to keep my feet on the ground, and I will do.
"I have got to deal with the pressure of people saying I am going to be the next thing.
"I have just got to keep going and doing what I do and keep the hunger. I will always have that when playing here."
Watt has been tipped to become a top player for club and country in years to come but he revealed he was never convinced that he would make it to the top.
He explained: "You never really believe you have made it. I have still got a long, long way to go to keep my place in the team and hopefully I can do that over the next two or three years.
"In football you are always learning. You are never going to be the finished article unless you are the likes of Messi or maybe Ronaldo.
"A few people around me like Jimmy Boyle, my old manager at Airdrie, told me I had the ability to go on and do stuff like this. I never believed them and I was always hard on myself.
"Now he is the one that looks smart for saying that. I never thought I would make this impact when I came to Celtic but football is a weird game and it changes fast."