Parkinson's men produced a lacklustre and limited performance throughout against the Saddlers as they fell to a two-nil defeat at the Coral Windows Stadium.
The morale-sapping loss means City are still very much looking over their shoulders as the League 1 season enters into its final month or so of fixtures.
Far from feel the pressure of the situation, however, Parkinson says City must now roll up their sleeves and show the fans and the rest of the division what they are made of.
Parkinson said: "We have to come out fighting - it is as simple as that.
"We have worked really hard to get into this division. The club - all of the players and staff here - have worked so hard to get us here.
"We have eight games to go this season and we have to make sure we come off the pitch after every one of them knowing we have given absolutely everything.
"In every way, shape and form, we have to have tried everything to get the result.
"I don't think we did that tonight (Tuesday) though.
"We will be looking at ourselves as staff because we don't want a repeat of that.
"Myself and Steve (Parkin) will be sitting down with the rest of the staff after the game now and going through what we can do from now until the end of the season.
"We have a great club here with magnificent supporters, who have backed us so well throughout the good times and the bad.
"Our supporters know when they see a fully-committed performance from the lads, and they didn't get that tonight."
Although it is ultimately no excuse for such a lifeless display, City's efforts weren't helped by the continued injury problems for influential striker James Hanson.
The forward wasn't deemed fit enough to start Tuesday's match and only featured as a second half substitute because of the Bantams' struggles during the game.
Hanson's back injury is something that has bothered the giant forward for a couple of weeks now and Parkinson admits City will have to look again at how they can get to the bottom of it.
Explaining his frustrations at the on-going situation, Parkinson added: "Hans had a fitness test ahead of the Colchester game. He didn't train before the Gillingham game and still played.
"It was the same story for the Shrewsbury game. He had another fitness test ahead of that one and he said that he was only 75% fit but still played.
"He didn't train Sunday or Monday and then had another fitness test tonight and said that he only felt at 65%. It is an on-going saga and we need to get to the bottom of it.
"He has been to see a chiropractor four times now and we still can't seem to solve this back problem and the spasms he's getting. We took on medical advice and left him out of the team tonight.
"I only actually put him on the bench because Olly McBurnie was a late withdrawal due to injury. I was only going to use him if I really needed him as well.
"The way the game was going though, I felt we really needed his physical presence up there."