Louis van Gaal refused to rule out Manchester United's chances of reaching the Europa League quarter-finals, despite admitting his side crumbled at Liverpool.
The Merseysiders took a firm grip of their last-16 tie with a dominant 2-0 victory at Anfield, courtesy of goals from Daniel Sturridge and Roberto Firmino.
Thursday's defeat leaves United's European aspirations teetering on the brink ahead of next week's second leg at Old Trafford, where an away goal for Liverpool would leave United needing to score four times.
Van Gaal was adamant the tie was not dead, although he was forced to admit United hopes rest on dealing with Liverpool's rampant high-pressing game, something which the visitors failed to do at Anfield.
"We did not cope with the high pressure of Liverpool," the Dutchman told his post-match press conference. "The pressure is not from the crowd.
"We had expected that and, for me, it was a surprise we did not cope with it because they did it at their home match this year.
"That raised the atmosphere in the stadium and they created big chances but we had a very good goalkeeper and because of that, we were in the match."
Despite this, Van Gaal was adamant the tie was not dead, urging United supporters to replicate the atmosphere Liverpool fans created and spur them into the last eight.
"We have to believe," he added. "We can also create an atmosphere [at Old Trafford] like Liverpool did tonight, so everything is possible.
"[The result] is disappointing, I cannot deny that. I don't think we were in the third and fourth phase very creative, but that's also down to the defence of Liverpool. You can give them credit for that. We have to improve a lot to score more goals."
Liverpool took the lead through Daniel Sturridge on 20 minutes when Memphis Depay was adjudged to have tripped Nathaniel Clyne in the area.
And Van Gaal took offence to referee Carlos Velasco Carballo's contentious decision, adding: "We get a cheap penalty and that was 1-0.
"Henderson was in an offside position [for the second goal] and when you are so sharp, you can see the foul has been made by Memphis in the area [for the penalty], you have to see also when it is offside."
He also insisted he was not aware of an apparent Marouane Fellaini elbow on Emre Can in the closing moments.
"I haven't seen it but I think also I have to say Fellaini was one of the best players on the pitch and I am very sorry when he makes a mistake like that," he remarked.