Already trailing against a dominating Barcelona side, United had to resort to physicality after 30 minutes to try to thwart the five-time European champions on Wednesday.
It helped prevent any further damage to the scoreline, as Barcelona won the first leg of their quarterfinal 1-0 after United defender Luke Shaw unwittingly helped Luis Suarez's header into the net in the 12th minute.
An equalizer never looked likely, though, with United failing to register a shot on goal in a Champions League game at Old Trafford for the first time since 2005.
Barcelona's goal — initially flagged for offside before being awarded via a video review — came during an exhilarating spell when the visitors' possession exceeded 80 percent.
"It was a great header from Luis," Barcelona coach Ernesto Valverde said. "He was fighting for every cause. He was getting stuck into the defenders, trying to work really hard."
But as Barcelona became sloppy and error-strewn, the early passing rhythm faded.
"We lost the ball in our own half a few times too often," Barcelona defender Nelson Semedo said. "But shutting down those errors gave us this big victory."
While the Spanish champions ended a six-game winless run on the road in European knockout games stretching back to 2016, this quarterfinal is very much still in play heading into the second leg on Tuesday.
So is the quarterfinal between Juventus and Ajax after the sides drew 1-1 in Amsterdam on Wednesday.
United only fleetingly imposed itself on Barcelona, but did so with force when Smalling escaped punishment for the foul which left Messi needing to clean up the blood on the touchline.
"This was a tough, complicated contest," Valverde said. "We dominated in spells but their pressure was high and difficult to break."
The closest Messi came to his first goal at Old Trafford was in the 83rd minute when the sting was taken out of a low free kick and it was easily gathered by David de Gea.
The United goalkeeper also denied Philippe Coutinho a chance to double Barcelona's lead in the first half when his left leg kept out the shot.
De Gea was also equal to Jordi Alba's strike in the second half to limit the damage.
United already came back from a heavier first-leg deficit to reach this stage, losing 2-0 to Paris Saint-Germain in the round of 16 before winning 3-1 in the French capital last month to help Solskjaer secure the manager's job on a three-year contract.
"The PSG performance away gives us hope and belief we can do it," Solskjaer said after United's fourth loss in five games in all competitions. "But we know we are playing against probably the favorites in the tournament."
In that first leg against PSG, United only managed one shot on target. Against Barcelona, the three-time European champions couldn't even hit the target once — the first time that has happened for them in the Champions League since 2005.
"For large spells we made it difficult for them but unfortunately we couldn't get the goal because we created a lot of good chances," Smalling said. "We had a little spell in the first half where we went after them but then we started to look a little bit nervy.
"I think from halftime we got at them, really pressed them and to be honest we caused them so many problems."
But now United will have to be the first team to win at Barcelona in 30 matches stretching back to 2013 if it is to advance to the semifinals.
The teams will have contrasting preparations for the second leg when Shaw will be suspended after being booked for tugging at Messi.
Barcelona on Saturday heads to Huesca holding an 11-point lead at the top of the Spanish league, but Manchester United hosts West Ham in the Premier League trying to climb up from sixth place to the four Champions League qualification places.