The Red Devils are hot on the tails of Roberto Mancini's side following a 2-1 victory over Arsenal after their North West rivals secured a 3-2 win over title challengers Tottenham Hotspur yesterday.
"We obviously heard the [Man City v Spurs] score before the game and it would have been nice for them to draw but we can't really rely on them to keep dropping points," Smalling told talkSPORT.
"We've seen Tottenham bursting forward over the last ten or so games and I think [the title race] will go down to the wire. This is the start of a really difficult run for us and this [win] is a great start."
Sir Alex Ferguson's side are three points adrift of Man City.