Having endured a frustrating spell on the sidelines with a hamstring problem, Wilkinson marked his comeback with a 95th-minute strike to seal a 2-1 victory over Salford City on Saturday.
And he wants the much-needed triumph to be the start of better things for the Saddlers in League Two.
"From minute one, we dug our heels into the ground and wanted the three points. That was the most important thing," said Wilkinson.
"We said before the game we don’t care how we get it, we need the three points.
"Teams don’t come here and outplay us. It is a simple fact of a set-piece, a free-kick or a corner, and we do play good football and create chances, and we will start hitting the back of the net very often.
"Hopefully, that has given us a little bit of a kick-start and we can go and really claim some authority in the league now."
Wilkinson was introduced by Matt Taylor in the 82nd minute and made the difference with a sweet left-footed finish.
"It was the hardest eight minutes of my life," added Wilkinson.
"Well, there was six added on, so it was a bit longer than that. It was hard, like a game of basketball.
"I was thrown on to make an impact, and luckily enough I did.
"The game was pretty open and I thought that if I could get one versus one, I would have a good chance.
"I’m always going to gamble and try to outsmart the keeper, and it’s worked."