The Red Devils fell to a convincing 2-0 defeat at the hands of Moyes's former club Everton at Goodison Park today, a result that leaves them 13 points behind the top four with four games left to play.
It was also United's 11th defeat of a miserable season, but Moyes insists that they are "rebuilding" despite his acknowledgement that the team's performances have not been good enough.
"I think everybody knows that we are on track to make changes and do some different things. We are rebuilding. I understand it has not been good, I recognise it has not been good, and it needs to be better," Moyes told reporters.
The last time that Manchester United failed to qualify for the Champions League was almost two decades ago in the 1995-96 season.