United were held to a 1-1 draw with Southampton on Saturday, with Che Adams's second-half strike cancelling out Jadon Sancho’s opener.
Ralf Rangnick’s side have now drawn their last two Premier League games by the same scoreline [1-1], and it has not really helped the push for a top-four place.
Shaw is under no illusions that it is imperative the side start getting more points on the board.
''We know it's a massive game against Brighton on Tuesday so our full focus needs to be on that,'' the 26-year-old told club media.
''We know we will have the fans behind us but we also know it's up to us to do it on the pitch.