The Bantams will book their place in the last four of the nation's most prestigious knockout competition for the first time in 104 years if they overcome Reading in a Saturday lunchtime kick-off at Valley Parade.
Victories over Chelsea and Sunderland have helped write another special chapter in the club's recent cup history and Parkinson is convinced it could rank as the best one yet.
Parkinson said: "The FA Cup is obviously a level above the Capital One Cup
If we can do it this time it will be the first time since 1911 and this group of players will be remembered.
"This is what being involved in football is all about, and the big teams from the Premier League will be casting very envious eyes on ourselves and Reading playing in an FA Cup quarter-final on Saturday."
Parkinson managed to protect his side's status as outsiders prior to the fifth-round win over the Black Cats and accepts it is harder to sustain the underdog mentality as the rounds go by.
And despite many neutrals expecting to see the Bantams sail through to the semi-finals, Parkinson warned that Saturday's showdown could prove even tougher than their two previous rounds.
"We are playing a team from a higher division who have been in the Premier League twice in the last nine years, and we are enjoying testing ourselves against these types of teams," added Parkinson.
"Right from the Millwall game through the Chelsea and Sunderland games we just speak to the lads about testing themselves and hoping to perform to the maximum.
"But we are under no illusions at all that to get through this game we are going to have to play probably better than we have at any point this season so far."
Former Chelsea defender Filipe Morais will face a late fitness test on a knee injury which has forced him to miss the Bantams' last three games.
Source : PA