Carrick was unable to relieve some pressure on his increasingly untenable position as Manchester United manager at Stamford Bridge.
United had plenty of chances to put the game beyond Chelsea in the first half but it all fell apart in the second.
£117 million man Morgan Rogers strolled past Martinez for Chelsea’s opener just a few minutes after half time for his sixth goal of the season.
When it rains it pours for Man United at the moment. Martinez was shown a second yellow for an unnecessary challenge on Wesley Fofana, conceding a penalty in the process.
Cole Palmer scored the spot kick and from then the game was beyond Carrick’s side.
After the game, TNT Sports asked Carrick if he felt he had been let down by Martinez, to which he simply responded: “No.”
“It has a major importance on the game,” Carrick later told Match of the Day. “A huge moment. I think that is pretty obvious really."