The Red Devils' 4-3 victory over Newcastle on Boxing Day moved them seven points ahead of rivals Manchester City at the top of the table, but they allowed the Magpies to lead three times before Chicharito's last-minute winner.
And now, at the mid-way point in the season, Sir Alex Ferguson's side have let in just five fewer goals than slipped past them throughout the whole of last term and the centre-half says they must improve.
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"We have to make a big effort to push on from a good position. If we're going to maintain where we are, we have to sort ourselves out.
"We seem to make sure the punters get their money's worth when they come to the ground at the moment.
"But it was a great show of character from the lads at the start of a really busy schedule. It was really important to get the win, no matter how we did it."
Despite their healthy lead over City, the 34-year-old says the title battle is by no means over, highlighting last season when Mancini's men clawed back an eight-point deficit to win their first league title in 44 years.
"A seven-point lead means nothing because we've been in positions over the years of being eight, nine, 10 or even 11 points clear and not gone on to win the title," he continued.
"We've also been behind and won it. It's a great result for us, other results also went for us, but we've got more big games coming up."
With the club's reputation for always finding a winning goal when drawing late in games only reinforced by the victory over Alan Pardew's side, the defender then moved to credit manager Sir Alex's attitude.
"The manager has got that never-say-die spirit and it filters down through the club," he added. "We take it out on the pitch and reflect that.
"All the way through the game we were creating chances and looked like we were on the cusp of scoring goals.
"It was really important to get the win. Their goalkeeper made a couple of good saves and we didn't finish off a couple of chances that we created.
"But we've always got confidence in our boys and in the fact we're going to score."