In an enthralling encounter, Fulham took the lead through Andreas Pereira before a brace from Mateo Kovacic put City in front.
Jeremy Doku then made it 3-1 to City before Rodrigo Muniz netted late on for Fulham, with City winning 3-2.
The outcome of the game could have been different had Traore not missed a couple of inviting chances to score.
Fulham winger Adama Traore revealed what Manchester City boss Pep Guardiola said to him
Traore, who knew Guardiola from his time at Barcelona, revealed that Guardiola gave him encouragement after the game and also offered advice on how to finish the chances that he missed.
The 28-year-old hailed Guardiola as 'the best coach in the world'.
Traore told El Larguero: 'I've known him for a few years, but it's always appreciated.
'He is the best coach in the world, without a doubt. After the game he came up to me to tell it was a good game, he gave me some pointers on how to finish the chances I had against them.'
Asked about Traore in his post-match press conference, Guardiola said: 'I met him at Barca. When I arrived at Aston Villa I also had a call with him and he has always been friendly.'
'Adama, he's unstoppable that game. We couldn't control when he had the ball. You have to defend in your 18-yard box.'
Traore represented Barcelona at youth level and made four senior appearances before signing for Aston Villa in 2015.
Spells at Middlebrough and Wolves followed, with Traore having a spell back on loan at Barcelona prior to joining Fulham in 2023.
Traore often poses a threat with his direct runs but he has scored just three goals in 26 appearances for Fulham so far.
Fulham are currently in eighth place in the Premier League having taken eleven points from their first seven games this season.