There has been a little progress this campaign against top-six clubs with a win at home to United, a draw at Everton and defeat at Arsenal.
The second-placed Reds head to Tottenham on Sunday knowing their credentials will be tested as they were when they went to the Emirates riding high and slumped to a disappointing 2-0 defeat.
Just to make things more difficult, Liverpool's last away victory came against rock-bottom Sunderland on September 29, in sharp contrast to their home form which has seen them score 20 goals in five successive Anfield wins.
Rodgers insists they can turn around their form against their rivals.
"They are difficult games. Of course we love playing at Anfield where we have our supporters behind us," said the Reds boss, who has already won more matches at home this season than in the whole of the previous campaign.
"You can see the confidence going through the team and that was a massive step forward for us.
"When you go away from home you are going to be up against it but our approach is the same.
"We go into every game to play well, to work the ball and work hard when we don't have it.
"You are asked different questions away from home and we just need to cut out the mistakes we make because it hasn't been teams who have opened us up, we have conceded disappointing goals or own goals.
"If we can cut that out then we know we have enough ammunition to get goals.
"I am confident we can win these games. We should've won a number of games last year away from home so that is where we will see the progress."
If they are to start competing, Liverpool will need to tighten up at the back having conceded in 10 of their last 11 league matches.
"We have made mistakes defensively. We own up to that. That has cost us goals, some of them cheap goals," added Rodgers.
"It is swings and roundabouts because we won the first three games 1-0 and people talked about our lack of goals - which I don't think is something you can level at this team.
"Now we are scoring it is the clean sheets. In these types of games where it is tight you have to make sure you don't make mistakes.
"It was something last year that cost us in terms of these big games where we were in front and made mistakes."
Any progress they can make over the next month must be achieved without captain Steven Gerrard, whose hamstring injury sustained last weekend in the 4-1 win over West Ham could sideline him for up to six weeks.
But Rodgers is looking for other players to compensate with improved performances.
"Him (Sturridge) being out is a miss. His stature and his quality we will miss but as a group we will come together," he added.
"We've had it here before; whenever Daniel Sturridge wasn't playing we won games, whenever Luis Suarez wasn't playing we won games.
"It is an opportunity for others to step up to the plate. The focus is on the overall squad and over the course of the next three weeks or so that won't be called into question.
"Luis is in great form at the moment, his quality and energy and robustness is where he comes into his own.
"He is remarkable and is up for every game so there is no worry there.
"We have enough talent in the squad means we can restructure the team a little bit but we have enough quality."
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