Criticism for United's poor results has been largely aimed at Van Gaal, but Smalling believes no one should feel safe.
"If anything we are all playing for our own futures as well," the England international told British media. "To say we're not playing for the manager is silly.
"Every week we want to go out there and show everyone what a good team we are and on our day we can beat anyone."
Smalling is one of the players whose performances have improved during Van Gaal's tenure, and he insists that the manager's demeanour remains unchanged.
"He has been himself from day one that we met him to how he is now," the 26-year-old defender, who is viewed as a future United captain by the Dutch manager, said.
The Red Devils have been heavily criticised for their rigid possession-based play, but were more positive during the draw against the Blues.
Smalling, however, insisted the manager was not going to change.
"He is not going to change and that is why he has had a lot of success throughout the years," the defender said, referring to Van Gaal's illustrious career with some of Europe's most prestigious clubs.
"I can't ever see him changing because he's got a track record."
United went into the Chelsea game amid intense speculation over Van Gaal's future, with some fans even wearing Jose Mourinho scarves. The sacked Chelsea manager has been linked with the Old Trafford hotseat.
Dutch media reported national team manager Danny Blind believes Van Gaal, who had led the Netherlands to the 2014 World Cup semi-finals, would be an excellent appointment as their football association's technical director.
(Reporting by Chris Peters in Bengaluru; editing by Sudipto Ganguly)
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