The Red Devils headed into a home date with their arch-rivals with a clearly defined plan of how they intended to set about claiming a positive result.
Those pre-match preparations were ripped up inside the opening 20 minutes as Marcus Rashford suffered a knock to his ankle and Ander Herrera was forced from the field.
Juan Mata then followed a fellow Spaniard to the dressing room before his replacement, Jesse Lingard, limped off on his return from a previous ailment.
Solskjaer admitted afterwards that “everything that could go wrong did go wrong” for his side, but United still had enough about them to tinker with their tactics and take a point from a 0-0 draw.
Lukaku claims that resilience is down to the message being put across by the manager, with the Belgian striker telling Sky Sports: "I think the coaching staff did a good job of telling us the indications of how to play and we were prepared for any situation.
"We did well as a team and, from this performance, what we have to take is that we can fight in whatever circumstances.
"If a player gets injured we can always make sure another player comes in and does a job, so I'm happy."
United are now waiting on updates from their medical department when it comes to the walking wounded.
They are due back in action on Wednesday against Crystal Palace.
Solskjaer may have to get creative with his selection for that fixture, but a man now unbeaten through 10 Premier League outings is being backed to keep the Red Devils competitive.
Asked if a dogged display against title-chasing Liverpool was another example of the progress being made under an interim coach, Lukaku said: "Yeah, of course.
"Everybody's been talking about us being offensively a great team, but I think defensively we are doing a great job, as well.
"Look at how the defenders are playing. Chris Smalling coming in for the last three games and doing really well, so he raises the level as well.
"For the defenders the competition is great and for us up front as well. We have to keep performing how we are and make sure whatever situation we have, we control the game and try to win."