The Gunners were thumped 5-1 at Anfield last Saturday lunchtime, trailing 4-0 inside 20 minutes as their defensive lapses in confrontation were punished by clinical finishing from the Reds.
Arsene Wenger's men recovered some stability with a goalless draw at home to Manchester United on Wednesday night, which provides a base from which to attack the FA Cup tie at the Emirates Stadium on Sunday ahead of a Champions League showdown with Bayern Munich next week.
Parlour - who played more than 450 matches for Arsenal, winning the double in 1998 and 2002 under Wenger - feels the Gunners must not allow any thoughts of what happened up on Merseyside when they run out against Brendan Rodgers' men again for Sunday afternoon's prime-time televised encounter.
"Being 4-0 down after 20 minutes away from home at a place like Anfield is a player's nightmare, so how do you bounce back?" Parlour, an ambassador for the Budweiser Open Trials campaign, which will provide amateur footballers with the opportunity to play at Wembley in front of professional scouts, told Press Association Sport.
"You do have bad days at the office and you just have to keep focused, get yourself right mentality.
"The clean sheet against United was a positive and Sunday's game will be vital.
"And if they can beat Liverpool, with the form they are in, then that can only give confidence for tackling Bayern Munich on Wednesday."
Parlour feels the FA Cup draw could open up for Arsenal if they can get past Rodgers' side.
"I know Arsene Wenger might have one eye on the Bayern Munich game next week, but this is a great opportunity," he said,
"Arsenal's home form has been pretty good and the Emirates Stadium is now much more of a fortress than when it first opened.
"It will be difficult because Liverpool are going to come there with a full squad, but if you look at it one of Manchester City and Chelsea will be knocked out, so there is a chance there."
It has been the best part of a decade since Patrick Vieira lifted the FA Cup at Cardiff, and performances this season in mounting a long-overdue sustained Barclays Premier League title challenge have lifted hopes 2014 could finally see Arsenal get their hands on some silverware once again.
Parlour - who scored a spectacular 30-yard opening goal against Chelsea in the 2002 FA Cup final - feels going on to win the famous old trophy once again would more than make up for those barren campaigns.
"It is a frustration for supporters after we won so much, but a lot has changed, the new stadium was always going to be a big thing and resources were always going to be stretched," the 10-times capped England international said.
"I think the manager has done a brilliant job, but now they have to start competing again and signing Mesut Ozil was a big statement of intent.
"But Arsene Wenger will be looking at this season as still having three good chances to win that trophy, which hopefully they can do to settle everyone down and then we can all look forwards to the next season."