Sir Alex has urged the Reds to keep the foot on the gas ahead of Boxing Day's encounter with Wigan Athletic.
The Latics have secured impressive back-to-back draws against Chelsea and Liverpool and, although they have still to take a point from United in the Barclays Premier League, there is no question of them being under-estimated at Old Trafford.
"I watched Wigan versus Chelsea the other day and I thought Wigan were terrific," said the boss. "It says a lot for Roberto Martinez - he continues to play good football irrespective of what position they're in. We have a good record against Wigan but we won't take anything for granted. We need to keep out foot on the pedal."
Sir Alex feels Martinez's men will avoid the drop because the match against Andre Villas-Boas' team recently showed a vast improvement on last season's display.
"I don't think they're a relegation team," he stated. "They do well against the bigger teams. Last year, I think they lost heavily to Chelsea [6-0 at the DW Stadium] and, this season, they got a draw and could have won. I think Wigan will stay in the Premier League.
As for United's own form, the manager is rightly proud of his team's reaction to some of the low points this season, including the derby day defeat to Manchester City and embarrassing exits from two cup competitions.
"The criticism has been understandable," he added. "You lose a derby game 6-1, you're knocked out of the Carling Cup and you lose to Basel, who aren't a powerhouse. You can understand the criticism.
"But we show the resililence and determination to do something about it, each time it happens. That says a lot about the character of the team."