After finding themselves two goals down with less than seven minutes on the clock, Parkinson's men clawed their way back into the match thanks to a first half double from Nahki Wells.
Coventry striker Callum Wilson fired the visitors back into the lead just before half-time, but Wells was on hand again to ensure a share of the spoils for the Bantams with a dramatic last-grasp penalty.
The thrilling draw, which was played out in front of the Sky Sports cameras, meant City moved up to seventh in the league table and remained firmly in the Play-Off shake-up.
Parkinson said: "We're started poorly and given a good side like Coventry a two-goal start. Coming after our performance and result at Rotherham last weekend, it certainly wasn't the ideal thing for us to do.
"But the way we responded after that was outstanding. We're got it back to 2-2 and we were playing some great attacking football. We're had chances, penalty appeals, free-kicks, all sorts of things coming our way.
"The third goal for Coventry knocked the stuffing out of us really. I think it knocked everyone in the stadium and in the team back a bit. Coming into the second half though, I just always felt we could get a goal.
"When the lad (Andy Webster) doesn't get sent off for handball when Nahki (Wells) is clean through, you just start to wonder whether it is going to be our day or not.
"In the end though, Nahki's put his penalty away well and we've got a deserved point from the game.
"We knew we would have to be tactically switched on today (Sunday) because Coventry are a good side, but we also knew that the mentality of the players was going to be key as well.
"The spirit in the side was right today.
"We've shown that same sort of spirit last season and earlier this season. I felt we've needed recently to get back to that again, and we did.
"Obviously we wanted the win, but when you're 3-2 down with only seconds to go, you'll take the point."
Wells' injury time penalty was the twelfth goal of the season already for the Bermudian - an even more impressive stat when you consider the striker was sidelined for a month earlier in the campaign with an ankle injury.
The goal - Wells' fiftieth for the club - also sealed his second-ever hat-trick for the Bantams following his treble at Northampton Town back in April 2012.
Parkinson said: "I thought Nahki has looked rusty the last couple of weeks because he's missed a lot of football. I could sense in training this week, however, that he was getting back to his usual sharpness.
"He was back today to the Nahki Wells we know in terms of his running with pace, his work-rate and his coolness in front of goal. I can't say I watched his penalty though! I just looked at the ground and waited for the crowd to react. Obviously though, I was so pleased when it went in.
"We wanted the media after the game to be speaking about the performances of Nahki and James Hanson instead of Coventry's front two (Leon Clarke and Callum Wilson).
"In truth though, it was probably even between the four of them because Coventry's front two have also played well.
"(Coventry manager) Steven Pressley is fortunate to have inherited two good strikers in Leon Clarke and Callum Wilson just like I am fortunate to have inherited James Hanson and Nahki Wells.
"I think today was certainly a game when the strikers were on form and the defenders not so much."