David Moyes' tumultuous time in charge of United continued on Saturday with a 2-1 loss to Stoke City.
The evenness of the top sides in the English Premier League this season means United are just seven points adrift of fourth-placed Liverpool despite their struggles.
Smalling said the time had come for United to start putting pressure on the teams above them with results.
"We've got to go into it as if we need to win every game," he said.
"We're the ones who have to catch the others so we've got to win the points and put the pressure on them.
"We've not done ourselves any favours with losses like this. We're not in those positions at the moment and that's a worry but there is plenty of football left.
"There's a lot to go but time is running out and we need to make sure we put things right come the next game.
"Each point that we drop makes it difficult for ourselves. Other teams will drop points as well but we need to stop ¬dropping points. We need to put pressure on other teams."
Smalling said the players understood a top-four finish was the minimum expectation for a team coming off a title-winning season.
The 24-year-old played down the pressure on Moyes by saying it was up to the players to turn United's season around.
"We don't really talk about it but we all know that's the minimum we need to aim for," Smalling said.
"It is only we players who can get us out of this muddle that we're in."
