Already under fire for throwing away winning positions at Fulham and Everton this season, the Red Devils shot themselves in the foot again at Old Trafford when they allowed Liverpool to claw themselves level from two goals down, even though the Merseysiders did not carve out a chance for themselves.
It took Dimitar Berbatov to rescue them by becoming the first United player to score a hat-trick against Liverpool since Stan Pearson in 1946.
The result keeps the Red Devils within sight of Chelsea.
As Evra acknowledges, United might still have been able to overcome Carlo Ancelotti's title favourites if they had dropped more points on Sunday. But the mental scars might have taken some recovering from.
"If we keep bringing that nervousness to the situation we could finish the game with a heart attack," said Evra.
"It wasn't that I was worried at 2-2. I was actually very unhappy.
"If we had drawn that game, how could we then say we were going to win the league.
"We had an accident at Fulham. We had another accident at Everton. But if you do it again it is not an accident. It is simply that you do not want to win the league."
It would be easy just to blame United's defence for the problems.
Yet new captain Nemanja Vidic has, by common consent, had an outstanding start to the season.
Indeed, the goals conceded at Craven Cottage and Goodison Park were from crosses at set piece situations.
On Sunday, a rash penalty box challenge from Jonny Evans and Darren Fletcher coming off the United wall at a free-kick were the reasons why Steven Gerrard was able to haul his team back into the contest.
"I don't know why we make the job hard when it could be so easy," said Evra.
"We have to make sure that kind of thing doesn't happen again. We need to make Manchester United solid.
"It is not only about the defenders. It is about everyone.
"We conceded two goals in a match where the opposition didn't even have a shot on target. That type of thing should not happen."
Six months ago, the thought that Berbatov would emerge the hero after dragging United out of their own mess would have been fanciful in the extreme.
The Bulgarian never entirely won over the United faithful following his club record £30.75million transfer from Tottenham two years ago.
Berbatov's arrival resulted in fans' favourite Carlos Tevez being left languishing on the bench, while Ferguson's belief that the 29-year-old would give his side an added dimension did not quite materialise.
It would not have been a surprise if Berbatov had moved on during the summer and even on Sunday, Ferguson was admitting this was a hugely important season for the striker.
Yet, with Wayne Rooney still searching for his scoring touch, Berbatov has filled the breach magnificently.
He had already scored four this season before Sunday's exploits, which included the magnificent overhead kick that left Pepe Reina rooted to the spot.
"He scores a lot of goals like that in training," revealed Evra. "I am not surprised.
"He can do so many things and I hope and wish he will carry on that way for the rest of the season."
Although Berbatov is not the most gregarious of characters, and had to be told by Ferguson not to dwell on the negative comments that were made about him such is his tendency towards introspection, within the Old Trafford dressing room it seems he is a popular figure.
"Dimitar deserves this because everyone knows he has such a big talent," said Evra.
"I have never been worried about his form.
"But he has had a hard time here. It has never been easy but he has continued to work very hard.
"It is not only against Liverpool that he has done well. It has been from the beginning of the season.
"He has everything in his game to be the best striker here. I am really happy for him."
Evra is almost certain to be one of those excused duty from Wednesday's Carling Cup tie at Scunthorpe.
Ryan Giggs is struggling with the same virus that ruled Rio Ferdinand out on Sunday, although he would not have been involved, while fellow veterans Paul Scholes and Edwin van der Sar will be given the night off as well.
Anderson and Darron Gibson will probably anchor United's midfield at Glanford Park, while Michael Owen will be given a rare opportunity, probably alongside Javier Hernandez, in attack.