"Liverpool tend to pull out big performances when the chips are down, and it was a fantastic effort to beat a strong Manchester United team on Sunday," said Murphy.
"It was considered a must-win game for the club and they went in surrounded by a huge amount of pressure.
"The result was great for them and great for the Premier League. It wasn't the most exciting game to watch in terms of spectacle, but Liverpool did what needed to be done.
"It may well be the confidence-booster they need to string a run of results together, and start applying pressure to the other sides at the top of the table.
"When they play at their best they will always highlight weaknesses in their opponents. They pressurise teams on the ball and deny them time to play, and that is exactly what they did at the weekend."