Moyes has come under increasing pressure in recent weeks, although Wednesday's Champions League victory over Olympiakos offered a timely boost following an embarrassing defeat against Liverpool three days prior.
The Red Devils will face Bayern Munich in the Champions League last eight, but are 16 points behind Premier League leaders Chelsea and were knocked out of the FA Cup at the first hurdle, and Scholes has warned that Moyes, like any United boss, will have to start improving.
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"You know, results are supposed to decide if he’s there, when he’s there, at United you’ve got to challenge for the league title, there’s no doubt about that, you’ve got to challenge for the FA Cup, and you’ve got to challenge for the Champions League, and if you’re not doing that year on year, whoever’s in charge won’t be there."
Scholes is sympathetic to Moyes' cause this season, however, and says he "feels sorry" for the Scot due to the amount of injuries he has had to contend with.
"It’s far too early [to sack him]," he said. "With all the injuries he’s had, I feel quite sorry for him really.
"He’s never been able to put out the same back four. You see all the top teams, they have the same back four every week, especially with the centre-backs, they need to get an understanding and rhythm together.
"Michael Carrick’s been injured, Robin van Persie’s been injured, key players have been injured [but] he’s not made any excuses and tried to get on with it and hopefully next year will be better."