But the Hoops kid insists that he doesn't want to be remembered as a one-night wonder but rather as a player who firmly made his mark at the club.
The teenager started the William Hill Scottish Cup tie with Raith Rovers as Celtic booked their passage into the quarter-finals of the tournament, but he knows that players are effectively auditioning now for a place in the squad for the last 16 Champions League tie against Juventus.
The Scotland under-21 international hit the headlines last year with his heroics against Barcelona and it had the twin effect of helping Celtic on their way to qualification for the knockout stage and thrusting the starlet firmly into the spotlight.
While his route into the professional game via Airdrie may have been an unconventional one, there is no self-belief problem where Watt is concerned.
"I don't think I am out of my depth at that level (Champions League), he said.
"I think I am doing all right but the hard part is keeping that going.
"I scored that goal against Barcelona but it's history now ... I want to make a name for myself at the club and just get my head down and be as successful as I possibly can."
Next week's game against the Italian giants is an opportunity for Celtic to test themselves at the premier end of the tournament.
Few would have expected them to qualify out of the group they were in but, having done that, Neil Lennon will attempt to instil a confidence in his players that they are capable of going one better than they ever have in the lucrative tournament.
In that sense, the transfer window closing with two of the best players still at the club, Gary Hooper and Victor Wanyama, was vital.
Watt, like every other Celtic punter, was delighted that the club were able to stand firm when Norwich came calling for the Parkhead top scorer.
"I wanted Vic and Gary to stay as much as any supporter did," said the striker. "We need them now. They are two big players for us and they have shown their quality in the Champions League this season.
"They have proved they are more than up for the test and we need that if we are to have any chance of doing well against Juventus."
There has been another bonus for Lennon ahead of Tuesday's game with James Forrest's re-emergence in the senior team.
The versatile winger has struggled to make the same impact he did last term because of a series of knocks and bumps, but as he showed with his goal against Raith on Sunday, his quality is not in doubt.
Watt is well aware that having a player like that fit and available for the game against Juventus strengthens Celtic's hand.
"He is a massive player for us," said the forward. "We need him back. He has every attribute to be a top winger. He is talented, he is fast, he is powerful, he can go by players, he has a good touch and a good cross and he can finish as he showed at the weekend. We were delighted to get him back fit because we need players like him."
In terms of domestic matters, Celtic will have the opportunity to take revenge on St Mirren in the Scottish Cup.
Danny Lennon's side wrecked Celtic's Treble ambitions when they bundled them out of the Scottish Communities League Cup at the semi-final stage. Having eased their way past Raith Rovers, a chance to atone for that Hampden defeat awaits.
"Hopefully we can go all the way in it," said Watt. "We just want to win everything that we possibly can."
The focus now, though, is inevitably on Saturday's game against Inverness in the Highlands, a match that is followed hard on the heels by the visit of Juventus.
Celtic will eye a positive result against Terry Butcher's side in order to go into the tie against the Serie A team in the best frame of mind.
"I need to prove to the gaffer that I'm good enough to be involved," said the teenager. "It was good to get a start at the weekend because it gave me a chance to work on my fitness.
"With the Juve game coming up, everyone is wanting to be involved and play for a place. We're looking forward to all the games that are coming up. The spirit in the squad is good and hopefully I can play a part in a successful season for the club. That's the aim."