Martial scored twice on Saturday to put United on the brink of victory at Stamford Bridge, only for Ross Barkley’s 96th-minute equaliser to earn Chelsea a late 2-2 draw.
The 22-year-old appeared set to leave Old Trafford in the summer when his agent Philippe Lamboley conformed he was unhappy in Manchester.
Martial’s relationship with Mourinho was understood to have become strained and his decision to leave the club’s pre-season tour to attend the birth of his child irked his manager.
On Saturday, however, Martial claimed there are no problems between him and Mourinho, who embraced him after he was substituted late on in the second half.
“Come on, things were not tense between us to begin with,” Martial said.
“We have a player-coach relationship and I hope that we will continue like that and bring Manchester United as much as possible."
Martial was delighted to spearhead United’s turnaround, having seen his side go a goal down to Antonio Rudiger’s first-half header, and believes United can take positives from the result despite their late disappointment.
The France international now has three goals in his last two games, following his equaliser in the 3-2 win over Newcastle United, and wants to maintain such scoring form.
“For sure. It has done me the world of good, of course,” he said. “However, ultimately, I am disappointed. We deserved to win but we shipped the goal in the last minute and it cost us."
When asked whether the result against Newcastle and Chelsea had eased pressure on United, he said: “For sure, we were not doing well. However, we worked hard and this sort of match enabled us to show that we are a good team.
“We want to continue with another good game against Juventus on Tuesday."
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