Helped by two Billy Knott goals, City were twice in front at The Den but they were eventually pegged back on both occasions during a thrilling 3-3 draw with the Lions.
The two sides will now meet again in the replay a week on Wednesday.
City looked to possibly be heading into Monday's fourth round draw outright when Knott gave Parkinson's men the lead again with only 14 minutes remaining but Ricardo Fuller's second of the match in the 83rd minute forced the replay.
Parkinson admitted afterwards that there was a slight tinge of disappointment in the Bantams camp after letting Millwall back into the game with time running out.
Given the fact that City were away to a team in a higher division than themselves, however, he knows his side still had plenty to be proud of due to the way they played at the home of an established Championship outfit.
Parkinson said: "There is a little bit (of disappointment) there. We feel we could have gone through and probably deserved to (go through). But we have to be pleased with how we have played overall throughout this tie and we look forward to the replay.
"We said before the game that it would be interested to test ourselves against Championship opposition and to see how we did against them.
"We also said we would come here with intent and with a positive attitude.
"I think we have done both of those two things we set out to do in the game. We've gone toe-to-toe with a decent side, who have quality in their ranks, and we've played in a positive fashion.
"We always looked like we could get goals today (Saturday). Equally though, they have real quality in that final third and they had their chances as well.
"There were different phrases of the game as the goals went in. They had their spells, we had ours, but the lads' response from going behind in the second half was absolutely magnificent.
"We got back in front with two quick-fire goals and then probably should have gone on and won it. We didn't but we at least go on to fight another day in this competition."
Despite the distance involved in getting to the match and the fact that the Christmas period has only just passed, over a thousand City supporters made the long trip down to London to cheer on Parkinson's men.
Their efforts were all the more commendable due to a serious motorway accident on the M11 that seriously hampered the progress of many Bradford fans trying to get to the game.
Parkinson added: "I have to give the supporters a special mention.
"Given the distance involved to get to this game and the fact we are just coming off the back of the Christmas period, I couldn't believe it when I heard how many tickets we'd sold.
"With the money that usually gets spent around this time of year, it would have been perfectly acceptable not to see too many visiting fans in the ground today. I have to say though that the support we did get this afternoon was magnificent.
"It was very important that we sent those supporters home with at least something to cheer about because it was a great turn-out by the fans."