Fulham are bottom with 20 points, four from safety, but Meulensteen feels they can fight their way out of trouble.
"The most important thing is we got a point," the Dutchman told Sky Sports television.
"A lot of people were classifying us as dead and buried. We have far too much quality and team spirit to be down there where we are."
Meulensteen's tactic of keeping 11 men behind the ball and looking to hit United on the break meant the hosts endured a frustrating afternoon.
Fulham led from the 19th minute, when Steve Sidwell stole into the United area unmarked to sidefoot home, until the 78th when Robin van Persie levelled.
Two minutes later the visitors were behind after Michael Carrick's deflected shot flew into the net.
"We made it very difficult for them," said Meulensteen. "They have some problems of their own in that respect. They kept creating chances and crosses but we defended fantastically well.
"You think at the end all the hard work will slip away. But for Darren Bent to score that equaliser it felt like a winner."
(Reporting by Toby Davis; editing by Tony Jimenez)
