As in the League Cup two years ago, City have stolen the headlines in the FA Cup this season with a series of famous upsets.
Wins over Chelsea and Sunderland have helped Parkinson's men into the last eight, with a club where he remains a fan favourite standing in the way of City's first FA Cup semi-final appearance since 1911.
"We don't fear them but we definitely respect them," he said on Thursday.
"Obviously we've got to take the experience of a couple of years ago and this season into the game. Looking at the lads, there's an air of confidence.
"We're enjoying testing ourselves against these teams, right from the Millwall game, the Leeds game in the League Cup, Chelsea [and] Sunderland.
"We're under no illusions at all that to get through this game we're going to have to play probably better than we've done at any point this season.
"We can't think too much of the prize of Wembley, we've just got to concentrate on the factors that are important in the 90 minutes."
Reading have not contested an FA Cup semi-final since 1927 but they could be without key trio Jem Karacan, Anton Ferdinand and Simon Cox at Valley Parade.
"No. Chelsea got beat. I won't speak to him, no," he explained.
"We'll talk [with the players] about how to beat Bradford, that's what we'll talk about. The rewards are there and clear to see, you don’t have to talk about them."
