Under his guidance, the Red Devils are seventh in the Premier League table, have exited the FA Cup, failed to win the League Cup and will need to overturn a 2-0 deficit against Olympiacos tomorrow night if they are to remain in the Champions League.
However, Moyes has insisted that the fans "will see great success in the future" with him at the helm.
"Results have been disappointing but it is not through lack of trying. The fans have seen some defeat they would not have expected and they have stuck with the team," he told reporters.
"They have seen great success and will see great success in the future. This club is the biggest in the world and it will rise again."
United have lost half of the 14 fixtures that they have played this year.