That fixture was their game in hand on defending champions Manchester City and has edged them into a one-point lead.
Jurgen Klopp’s side have looked down on the rest of the division for long periods this season, but have been held in four of their last five games across all competitions.
It has been suggested that the pressure is starting to show for a side that has gone 29 years since it last secured domestic dominance.
Scholes knows all about getting over that line, having enjoyed 11 title successes in his distinguished career, and feels the wheels may be coming off at Anfield.
He told Premier League Productions when asked how important City’s recent experience of claiming the crown could be: “I think it could be an advantage for City over Liverpool because with Liverpool you’re talking 20-odd years without winning the league.
“There were times when we [United] won the league a few times and then there was a year when we had a good lead and blew it, a couple of times that happened, but we’d been there before and it didn’t really affect those things.
“I just think the timing now – Liverpool drawing four out of five games – I think City are starting to hit real form. If I was Liverpool now, I would be worried.”
Liverpool have more testing fixtures approaching over the coming weeks.
City also have domestic and European action to take in, but their schedule is considered to be less demanding and Scholes believes they could start to pull clear of the title-chasing pack.
The ex-England international added: “Once you get into February, early March, that’s when you start to think about who you have got in the next few games.
“City will be looking at that and thinking there are four or five games that they are going to win. They will be thinking they could have a little lead in five or six games' time.“
City are set to play host to West Ham in midweek before taking in a run of matches against Bournemouth, Watford, Schalke, Swansea and Fulham.
They already have a first piece of silverware wrapped up, having overcome Chelsea in a Carabao Cup final penalty shootout, and are now looking to add the Premier League, FA Cup and Champions League to a possible quadruple.