Manchester United manager Jose Mourinho told his players at half-time that they risked looking like "clowns" if Manchester City were awarded the Premier League trophy after beating them.
City, needing a victory to confirm the title, were 2-0 up at the break at the Etihad Stadium thanks to goals from Vincent Kompany and Ilkay Gundogan.
But United produced a stunning revival to turn the match around, with Paul Pogba scoring twice in quick succession to equalise before Smalling thumped home the winner.
Speaking about Mourinho's words at the break, the defender told Sky Sports: "He didn't have to say too much, because deep down we know as players that wasn't good enough.
"He emphasised we don't want to be the clowns who are sort of standing there watching them get their trophy.
"You saw us stand up, coming in 2-0 down at City where they've been fantastic all season -- we stepped up and won the game.
"Coming in at half-time a lot of us were feeling sorry for ourselves.
"We needed to make sure we played with pride in that second half, and certainly deserved it with that second-half performance.
"The first half was terrible, apart from the first 15 minutes when there was nothing in it. Then we just dropped off and we didn't play our game and we could have been out of sight."
Smalling, who lost Kompany for the opening goal, said he had been pleased with his response.
"When you make a mistake like that you want an opportunity to make amends, and luckily it came today," he added.