City moved into the Play-Off places for the first time this season after a hard-fought point against Tony Mowbray's table-toppers - a result which extends the Bantams' unbeaten run to ten games.
Adam Armstrong hit the post for Coventry in the first half, whilst Rory McArdle and Tony McMahon went close for City either side of half time.
Ben Williams produced two important saves in the game's closing stages to deny Ryan Kent and Jacob Murphy and ensure City kept a seventh consecutive clean sheet in all competitions.
Parkinson said: "For a 0-0, it was quite a decent game. Two good sides going toe-to-toe.
"There were two sides out there on the top of their game working hard to stop the other side scoring while also working hard to create chances for themselves.
"We knew going into the game that Coventry had been scoring freely of late but I thought we did great against them.
"Tony's had a good chance well saved by their 'keeper in the second period. Their main chances came about really when we were a bit careless in possession slightly.
"All in all though, I couldn't have asked much more from the players.
"They worked tirelessly, and this is another good point for us.
"You always want to win every game you go into but it was a big ask of some of the players tonight (Tuesday), especially those who have played a few games now having not been in the team before.
"We can get the lads rested up for Saturday now and really go into that game on full throttle. Walsall will be another big test for us but we want these type of games.
"There was a real atmosphere and sense of anticipation around the ground tonight given the recent run both teams have been on."
Parkinson reserved special praise for his skipper Stephen Darby after the Bantams right back was forced to deal with a number of Coventry's key players at various points of the night due to tactical tweaks by the Sky Blues.
Parkinson added: "I have to give Stephen enormous credit because three of Coventry's key players - Adam Armstrong, Jacob Murphy and Ryan Kent - all played on the left hand side against him at some point during the game.
"He saw them all off, and it was an outstanding one-on-one individual defending performance from Stephen.
"Certainly in the second half when they have brought on Kent on to go up against him, it was a big test for Stephen and his fitness.
"Given the pace of Kent and his fresh legs having just come on, Stephen's fitness and concentration levels were superb and I thought he was outstanding."
Darby was joined in City's starting line up for the Coventry fixture by James Hanson after the striker recovered quicker than expected from an ankle injury.
Parkinson continued: "Hans put himself up to play.
"The ankle improved quickly over the weekend and he was able to do some training yesterday (Monday).
"Jordan Bowery came in and did well on Saturday but he was cramping up after about 65-70 minutes and it can be hard to ask loan players to go again just a few days later if they haven't played much recently.
"We didn't want to put him at risk in terms of injury so we just felt it was the right call to bring James back in and use Jordan off the bench."