United face the side currently propping up the Barclays Premier League at Old Trafford on 9 February in the wake of the 2-1 defeat at Stoke, and Smalling knows the Reds cannot let valuable points go astray this season.
"Each point that we drop makes it difficult for ourselves," he said. "We can only take the next game as it comes, and other teams will drop points as well, but we need to stop dropping points. We need to put pressure on other teams.
"We've got Fulham and then Arsenal so we've got some big games. We're back at Old Trafford next week and hopefully the fans will get right behind us and that will lead us into the Arsenal game."
United's defeat to the side marshalled by former Reds favourite Mark Hughes means David Moyes' men could be nine points adrift of fourth place by the time Fulham visit Old Trafford, but Smalling is positive about the prospects of securing Champions League football for next season.
"We don't really talk [about the Champions League] but we all know if anything that's the minimum we need to aim for. If we can get on a good run, we've got the players - obviously we lost a couple on Saturday, but we've got a week now until we next play so hopefully we can patch them up and get as many bodies out there as we can."
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