Van Gaal, who has spent over a quarter of a billion pounds since taking over 18 months ago, has overseen seven goalless draws this term and his team are five points adrift of fourth place with half the season to go.
But there is no sign that United are ready to wield the axe just yet and the Dutchman himself said following the Chelsea match that he had no plans to quit.
Van Gaal revealed he had already begun discussions with executive vice-chairman Ed Woodward about January transfer targets, and Smalling knows that could affect him and his team-mates after they embarked on their worst run in 26 years.
"To say we're not playing for the manager is silly," the United centre-back said.
"If anything we are all playing for our own futures as well, so there's not a case of no one not playing for the manager.
"And every week we want to go out there and show everyone what a good team we are.
"No matter what, whether it is good or bad, this club is always in the spotlight, and we've rolled our sleeves up, worked hard on the training field and had to make sure that we regrouped, especially after that loss against Stoke, so against Chelsea we stood up and showed that we were the better team, albeit we didn't get the win."
Van Gaal is such a confident character that hearing him speak about the possibility of resigning after the 0-0 draw at Stoke on Boxing Day came as something of a surprise.
The former Ajax and Barcelona manager sounded as if he had accepted the idea that he would leave the club.
But Smalling insists there has been no change in his manager's demeanour.
"No, he has been himself from day one that we met him to how he is now," the defender said.
"He is not going to change and that is why he has had a lot of success throughout the years. I can't ever see him changing because he's got a track record."
The England international, arguably United's best player this season, admits he and his team-mates are in real need of a win.
He hopes Monday's encouraging performance, in which they should have taken all three points following a thrilling first-half display, will help United end their eight-match winless sequence when they host Swansea on Saturday.
"We need that win because we want to stick at the top end of the table and, when you dominate games like the one against Chelsea, you need to win them, but we will take the positives and really make sure that next week we get the win," the 26-year-old said.
"Now hopefully this will give us that little boost that we can play well and kick on."
United set out to please their frustrated fans against Chelsea and Morgan Schneiderlin does not believe they could have done any more.
United at least brought an end to a four-match losing run but are now eight without a win.
As well as results, supporters have vented their anger at United's style of play, particularly a lack of attacking threat.
Schneiderlin said: "We talked before the game and said it was a must for us to be aggressive, to be on the front foot and to attack, just for our fans because they deserve to see some attractive football.
"Sometimes we can't do that for whatever reason but we created some magnificent chances and for everyone in the crowd I think it was a beautiful game.
"For us it was a good game as well because Chelsea are a very good team. But it will be hard to sleep because we didn't win."
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