Walker's post followed Man City's 3-1 derby win over their crosstown rivals.
Defeat leaves United in eighth place and with a negative goal difference, and City midfielder Bernardo Silva, who set up his side's first and third goals, suggested they are nearly out of the title race, as he warned their neighbours they now have no margin for error.
"It won't be easy".
"Man City, Liverpool, Chelsea, Arsenal, Tottenham, they have numbers to be champion".
"One team [City] started the season strong and are still strong, another team [United] didn't start well and is improving a lot", he added.
"I'm completely happy", Liverpool manager Juergen Klopp told reporters.
The break will give United boss Jose Mourinho time to address his team's problems - including shipping 21 goals after just 12 league games for the first time since 1966.
City, on the other hand, have won 10 of their 12 league fixtures this season to top the pile.
"We knew that there is a difference in potential (with City)", said Mourinho, whose side finished second in the Premier League last season, albeit a record 19 points behind City's 100-point tally.
Klopp: Liverpool have to apologise for the way they win
Liverpool v Fulham will also be available on the award-winning BT Sport app from this time onwards. And their imperious home form has shown no signs of relenting this campaign.
Victory over Manchester United saw the reigning champions return to the top of the table, re-establishing their two-point advantage over Liverpool.
"In the dressing room at half time, we had spoken about what happened in the derby past year, and we were telling each other not to let that happen again", the France worldwide said.
Palace winger Wilfried Zaha suggested he would have to get his leg broken by an opponent for a red card to be brandished following a 1-0 win over Huddersfield Town on September 15, at which Marriner was the fourth official.
"I consider the performance to be one with mistakes, it's different to a bad performance".
The last global break of the year means no game now for fortnight with the champions resuming a week on Saturday away to West Ham United. We didn't want to attack and they defended well.
"We were in a fight to try to get the equalizer", Mourinho said.
"In the second half the game is a bit open so we have to find more space but we made a good performance against a top, top team".
City have scored 12 goals in the previous week alone, so it was little surprise to see the home side go for the jugular once more.
Juergen Klopp's side made hard work of it for 40 minutes, however, and could easily have fallen behind.