The champions remain marooned in seventh place, seven points off fourth-placed Liverpool and England's final spot for Europe's premier club competition, following Saturday's 2-1 defeat by Stoke City.
The Old Trafford club last missed out on Champions League qualification 19 years ago.
"Each point that we drop makes it difficult for ourselves," Smalling told the club's website on Monday.
"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.
Although the arrival of Mata from Chelsea and the return of Rooney and Van Persie from injury briefly raised spirits at Old Trafford, United still have injury problems, with Rio Ferdinand and Nani among players still sidelined.
They also lost defenders Phil Jones and Jonny Evans during the Stoke match, with the former suffering concussion and the latter a calf problem.
"We don't really talk (about the Champions League) but we all know if anything that's the minimum we need to aim for," Smalling said.
"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."