Luke Shaw’s 12th-minute own goal means Barcelona will take a 1-0 advantage into next Tuesday’s return leg at the Nou Camp, where Ernesto Valverde’s side will be confident of progression.
United recovered after that poor start and managed to shut out Lionel Messi and his team-mates for the remainder but also failed to truly threaten their visitors.
“We pressed them high and made it difficult,” Smalling said. ”It’s a shame we couldn’t get the goal. I thought we created some good chances.
“We had a spell in the first half where we went after them and then we looked nervy, but after half time we got at them.”
Smalling added: “The whole team, we nullified them. 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.
“It was a good battle, my yellow card on Luis Suarez out of all the challenges I thought it was the softest.”
Smalling was one of United’s more impressive performers on a night, with Scott McTominay also catching the eye in midfield.
Ole Gunnar Solskjaer, the United manager, will be hopeful of another second-leg turnaround in order to play either Liverpool or Porto in the semi-finals.
United reached the quarter-finals after a remarkable turnaround away from home against Paris Saint-Germain, progressing on away goals after a 3-1 second leg victory.
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