An own goal from Luke Shaw was enough for the Spanish giants to edge the first leg, in what was a pulsating atmosphere at Old Trafford.
Ole Gunnar Solskjaer has now won just two of his opening six games as permanent boss, adding further pressure to United's upcoming fixtures.
Barcelona have been in decent form as of late, despite not firing on all cylinders by their extremely high standards.
Ernesto Valverde's side - despite being an under-strength 11- drew 0-0 with rock-bottom Huesca in La Liga on Saturday, not the best preparation for United.
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One player who has struggled since signing for Barca, Philippe Coutinho, came on in the 67th minute but was once again largely ineffective.
The Brazilian's inability to settle in Spain has caused various clubs to keep an eye on his status with a potential chance to gain his services.
One of those clubs were Man United, but after the two sides played their first leg it seems that the 26-year-old is against the idea.
According to Sport, Coutinho does not want to betray his former club Liverpool and after being the target of boos from a portion of the United faithful, the Brazilian is said to now be looking elsewhere.
Coutinho played more than 200 games in all competitions for the Merseyside club and would certainly tarnish his reputation with the side.
The former Liverpool player will be hoping to perform well against old rival, not only to win over a very demanding Barcelona fan base but to also give a nod to a side that held him in such high regard for six years.