During United's 1-0 victory at Old Trafford, Martinez in one moment of the game was able to hold off Traore who is one of the quickest and most powerful players in the Premier League.
After the game, Martinez gave a post-match interview in which he told Sky Sports pundit Jamie Carragher that he 'sent him (Traore) to the gym'.
Posting on Instagram, the Spanish forward has sent a six-word reply to the Argentine defender.
'Don't worry we will met [sic] again @lisandromartinezzz,' Fulham's speed merchant wrote with a winking-face emoji.
United beat Fulham 1-0 at Old Trafford in the opening game of the Premier League season on Friday. A single goal from youngster Joshua Zirkzee got Erik ten Hag's Red Devil's new season off to a positive start.
Martinez was up against Adama Traore on the left of United's defence for much of the game, with the Fulham winger initially getting the better of him to create a chance for the visitors.
Later on, Martinez got his revenge and brushed aside the Spaniard, eventually coming out the winner in their battle as he helped United secure the clean sheet.
After joking that he sent Traore - known for his strength and muscular physique - 'to the gym,' Martinez added: 'I learnt from the first one where he killed me. I killed him back.'
Carragher was complimentary of the defender after he finished the interview, with Neville saying he should speak publicly more often.
Martinez made just eight Premier League starts for United last season in an injury-hit campaign, but is now fully fit for selection.
'He has given you a tactical insight in terms of the team and other players,' Carragher said. 'He didn't come on and make excuses.
Carragher joked that Martinez, who is 5ft 9in, is 'virtually the same size' as himself, at 6ft 1in
'We criticise players and give them praise. He was heavily criticised and said he didn't play his best, but that type of personality to front it… he is a warrior, I thought he came across brilliantly.'
Roy Keane, meanwhile, added: 'It takes players a while to settle into the club, we should sometimes give players the benefit of the doubt.'