A first-half Luke Shaw own goal proved decisive at Old Trafford, as the left-back glanced Luis Suarez's header past the helpless David de Gea.
United could find no way back into the tie and now must win at Camp Nou to keep their hopes alive following their 1-0 defeat in the quarter-final opener.
Smalling preferred to focus on the positives, however, and saluted his defensive companions for a resolute display.
"The whole team, we nullified them,” Smalling said to
“I think there was only one other save for David de Gea. We knew we had to bring that intensity that they’re not used to."
United manager Ole Gunnar Solskjaer singled out midfielder Scott McTominay for his performance against the reigning Liga champions.
"Fantastic," Solskjaer said of McTominay on BT
"He's a great athlete, he can run all day long, he wins challenges, he's quick on his feet and today with the ball he was composed, brought the ball down a few times. He started settling us, to be fair."
McTominay was in a fiery mood after the game, accusing United of showing Barca too much respect, before also reminding their opponents that the tie is far from over.
"In the first 10, 15 minutes we showed them far too much respect in terms of how we set about to go and press," McTominay added.
"We're Manchester United, you can never write us off. They've top class players, but so have we and we're going to showcase that in the second leg at Camp Nou."