The 18-year-old winger played a starring role at the Emirates Stadium on Saturday as Arsene Wenger's men recorded a 2-0 victory over their arch-rivals.
After the game, Wenger hailed Gnabry but challenged the German youngster to show greater consistency.
And the teenager has pledged to take his manager's words on board.
"I'm just grateful that I've heard I put in a good performance," Gnabry told Arsenal's official website.
"I think that as well as I've done, I can always do better."
Gnabry, who made only his fourth start for Arsenal against Tottenham, was particularly pleased to have impressed against his club's biggest foes.
"I always want to win against Tottenham. I feel great to have put in a good performance to help the team to win," he added.
"Of course you are more motivated [against them] than to play against any other team in the Premier League and to win against Tottenham is a big thing for every Arsenal fan and every Arsenal player.
"It feels great as a young player to start in a game against Tottenham in a big derby - it's a great feeling. I just tried to do my best and help the team to win."
‘He instantly popped into our ratings as one of the best U21 midfielders in Europe. The impressive thing is Slot has made him into more of a no.6' Inside Ryan Gravenberch's transformation at Liverpool
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
