Knott twice fired City into the lead, but Riccardo Fuller ensured the Lions lived to fight another day with a second-half double.
“He (Knott) is an exceptional player in that position,” said Parkinson. “He’s played there for England Under-20s.
“He has that class in and around the opposition penalty box and you always feel he will get a goal.”
Knott fired City ahead from James Hanson’s knock down after six minutes only for Scott McDonald to level before the break.
Fuller’s first goal put Millwall ahead for the first time midway through the second half.
City responded, making it 2-2 when Hanson’s effort from long range bounced down off the bar and in off defender Sid Nelson and went in front when Knott volleyed home from Filipe Morais’s cross.
The home side were not finished and Fuller’s second set up a replay a week on Wednesday.
“I said before the game that I would be interested to see how we stood up against a Championship-quality side and I also said we would come here in a positive mindset, to play attacking football,” said Parkinson.
“We certainly held our own and probably should have won the game, and we were really positive every time we got the ball.
“At 3-2, it would have been great to have been in the hat outright, but we are in the hat and that was important.”
Millwall: Forde; Dunne, Shittu, Nelson, Briggs; Abdou, Chaplow (Gueye 81), Upson (Woolford 89), Martin; Fuller, McDonald. Unused substitutes: King, Powell, Martinez, O’Brien, Easter.
Bradford City: Williams; Darby, McArdle, Sheehan, Meredith; Halliday (Kennedy 77), Liddle, Knott (McBurnie 90), Morais; Hanson, Stead (Zoko 89). Unused substitutes: Routis, Mottley-Henry, Wright, Urwin.
Referee: D Webb (Lancashire).
Man of the match: Billy Knott.