After the third-round draw handed Crawley a home clash with the Royals, Barker watched their game against the Gunners and saw Arsene Wenger's side run out thumping 5-2 winners.
Reading will not be relishing the trip to West Sussex having collected just two points on the road this season, while manager Brian McDermott's priority is clearly survival in the Premier League.
But Barker knows his League One outfit will have to rise to the challenge to add the Royals to their collection of cup scalps in recent years.
"I saw them play Arsenal and if we play like Arsenal we have got every chance," he told reporters.
"They have a very strong squad, although I'm sure if the choice was beating us or Premier League survival then Brian would go for the league every time.
"But they are a very good side with some talented players and if we are to do anything we will have to be at our very best."
Crawley have beaten higher-division opposition in Hull, Bristol City and Derby in the FA Cup over the past couple of years.
They have yet to claim a top-flight scalp, but came agonisingly close in the Capital One Cup this season when, having already seen off Millwall and Bolton, they lost 3-2 to a stoppage-time goal against Swansea.
"A few of our players came of age that night and having had a taste of it we will have an idea of what to expect," Barker added.
"We had a game plan that night and it will be the same on Saturday. We will aim to still be in the tie after an hour and go from there."
Barker can also call on the inside knowledge of Crawley's director of football Steve Coppell, who guided Reading into the Premier League in 2006.
"Steve will have his usual input," Barker said. "I'm sure it will be quite a strange occasion for him but he is looking forward to the game as we all are.
"We know they are used to playing in front of tens of thousands every week in the Premier League, but 6,000 tightly packed in at the Broadfield is something different."