The Red Devils have won just two of their opening Premier League matches, while losing to Crystal Palace, West Ham and Newcastle.
Ole Gunnar Solskjaer’s side are two points above the relegation zone and face leaders Liverpool after the international break.
Rashford, who has not scored from open play since the opening day of the season, took to Twitter to address disgruntled Manchester United fans.
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He said: “You can’t hide in football and the last few weeks simply haven’t been good enough.
“As a United fan myself, that hurts. And you deserve better.
“We know we need to improve and that is our sole focus as a team and as a club.”
Rashford has struggled as United’s main striker following the departure of £72million-rated Romelu Lukaku in the summer.
Anthony Martial played through the middle at the start of the season, but the forward has been sidelined with a thigh injury for over a month.
It has piled responsibility on to the shoulders of Rashford, who has not scored in five games.
Solskjaer issued a public apology to United supporters following Sunday’s 1-0 defeat to struggling Newcastle.
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