Jose Mourinho's United recorded just 35% possession — their lowest in a Premier League game since Opta began recording statistics in 2003/04 — but held Liverpool to a 0-0 draw at Anfield on 17 October.
Zlatan Ibrahimovic spurned United's best chance of the game early in the second half at Anfield, miscuing Paul Pogba's cross at the back post and directing it across the face of Loris Karius's goal.
At the opposite end, David de Gea made excellent saves to keep out long-range efforts from Philippe Coutinho and Emre Can as Liverpool's winless run in the league against United extended to five matches.
Writing in the Liverpool Echo, Aldridge said he hoped to see a more open and exciting game against Watford at Anfield on 6 November.
"Watford have had some good away results this season, you can't take them lightly. They turned us over last year at Vicarage Road," he wrote.
"They'll come and get men behind the ball but their manager does like to play some offensive football so hopefully they will come and make a game of it unlike some others who have come to spoil and grab a point.
"I can understand teams being scared of our pace and movement, mind."
Liverpool are level on points with league leaders Manchester City after 10 fixtures and are on a 11-game unbeaten run in all competitions.
Aldridge talked up the Reds' title chances, saying they are "one of four teams" that can finish at the top this season.
"There's no reason for fans not to look towards the top of the table though and as a player and a manager if you're not looking to head to the top something's wrong with you," he wrote.
"We won't get carried away but you've got to go for it and see where you end up."