The Saddlers showed brilliant resolve to draw 1-1 with the much-fancied Bantams on Saturday, playing with 10 men for the entirety of the second half after captain Joss Labadie’s straight red card.
They had also had disappointing news going into the game as Wilkinson pulled his hamstring in training on Friday.
Walsall defended superbly to make it two games unbeaten in League Two and on whether they are heading in the right direction, Taylor said: “It’s only two games, so let’s not get carried away.
"But this is a performance that I think, as a group, they needed.
“It strengthens those bonds they have with each other, strengthens those relationships.
“You’ve still got to remember that the group is really new.
“But to see them perform in that way, to see them be organised when we had to surrender space, it gives you extreme pride.
“What we couldn’t do was surrender space in the middle. We had to surrender it out wide and trust we would deal with the crosses into the box – and we did do.
“They missed a few chances but Carl (Rushworth) didn’t have to make an outstanding save during the game, so that tells you we’re doing our jobs.
“I’m really happy with the players and their application.”
Jack Earing got the goal for Walsall in a gutsy performance at an almost 16,000-strong Valley Parade.
On Wilkinson’s condition, Taylor added: “He pulled his hamstring after about 15-20 minutes of training.
“We didn’t see it coming and, unfortunately, we don’t know what’s going to happen with Conor as of yet.
“What we do know is that we’ve got players that can step up to the mark.
“It’s disappointing that we’ve lost Conor, but what we can’t do is dwell on it as we’ve got a group of men in there who have worked extremely hard to get the opportunity.
“We’ll re-evaluate Conor during the week and do the best we can to get him back as quickly as possible.”