Tony Adams' men have won only one of their last eight games in all competitions – a 3-0 success against Dutch side Heerenveen – and Johnson believes City have the right mentality to cause a Cup shock.
Johnson said: "I'm hoping that at Ashton Gate we can take the game to them because the onus is on us on home territory. We aren't going to sit back and hope they have an off-day. We have got to make sure we get at them so they have an off-day."
Johnson conceded that halting Crouch would be key to success. And the Championship side have been boosted by the return from injury of 6ft 5in defender Jamie McCombe, who was highly effective against England striker Crouch at Fratton Park.
Adams will turn to the relatively unknown Arnold Mvuemba to spearhead his side's FA Cup defence as the Portsmouth manager battles a mid-season midfield injury crisis.
Sean Davis failed to report for training after being struck down by a stomach bug over the weekend and has been ruled out.