After Manchester City were held to a 0-0 draw by relegation battlers QPR on Tuesday evening, the Red Devils have the opportunity to open up a seven-point lead at the top when they face Southampton on Wednesday.
However, the Scot does not expect United's quest for the title to be a simple one, and described the upcoming fixtures as "massive".
“Teams will drop points. Not just us. Manchester City will drop points - absolutely, it’s a certainty. Chelsea and Arsenal will drop points," he told reporters.
“We’ll probably drop two or three ourselves, but the important thing is accepting the challenge that every game is just as difficult as the rest.
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“So we’re not taking anything for granted. We’ve got Southampton, then we go to Fulham and then it’s Everton at home. These are big games, massive games.”
The 71-year-old went on to admit that he knows little about his opponent on Wednesday night, newly appointed Saints boss Mauricio Pochettino.
“Yes, I’ll get some information,” he added. “I don’t know a lot about him to be honest but I will have a chat with my brother as he’s been scouting in Spain.
“It won’t matter in this particular game, as he’s just at the club, but they had a fantastic response against Everton.
“They should have won as they were superb and could have been five-up in the first half. Tim Howard had a fantastic game in goal for Everton."
Sir Alex also expressed bemusement over the south coast club's decision to sack Nigel Adkins in order to hand Pochettino the reins.
“I spoke to him the day before he was sacked. He phoned me about his situation there," he continued.
“I mean, I can’t understand these things. I think their form had picked up. What was it. two defeats in 12 games? That’s not bad for a team at the bottom of the league.
“Southampton’s fans have got a way of demonstrating and there were a few banners up at the Everton game.
“It’s nice in terms of recognising the contribution Nigel made. He brought them up into the division and it’s not an easy job.”