Even if the goal comes courtesy of their arch-rivals Melbourne Victory in the latest edition of the "Big Blue" at Allianz Stadium on Saturday night.
"It's not like when we do concede we're going to fall in a heap," Wilkinson told The World Game.
"We'll just go about our business again and everything will be normal.
"It's a great record to have, defensively, and hopefully we can keep it going for as long as possible, but it's not putting any extra pressure on the boys at all."
The Sky Blues have the best attacking and defensive record after the first four rounds of the A-League, with 11 goals for and none against.
They are also yet to concede a goal in four FFA Cup games to reach the final.
The last team they would want to break the streak against would be Victory, particularly playing at home, but Wilkinson, who is stationed alongside Matt Jurman in the central defence, said he knows it's going to be a busy night.
Training on the brilliant surface at @AllianzStadium today ahead of Saturday’s #BigBlue 👌 #SydneyIsSkyBlue pic.twitter.com/CDJJSUlba5 — Sydney FC (@SydneyFC) November 3, 2016
Victory striker Besart Berisha has scored four goals in the last two rounds and wingers Marco Rojas and Mitch Austin were also among the goals in the team's 6-1 win over Wellington Phoenix in Melbourne on Monday.
"We all know Berisha's a dangerous player, he has been ever since he came out here to play in the A-League," Wilkinson said.
"I suppose it's going to be a busy night for myself, but if the boys up front and in midfield can work hard to press Victory and not give them too much time on the ball it makes it that much harder for Berisha and their other front guys to get into the game.
"That's what we've been doing all along, the whole team has been working very hard in defence."
Wilkinson is 32 and a former Socceroo, but he is still experiencing plenty of firsts in the game.
Last season he played in his first Melbourne derby, for City against Victory, and in the first round of this season he made his Sydney derby debut against Western Sydney Wanderers. Now comes his first Big Blue.
"It's exciting for me," Wilkinson said. "The Big Blue is always billed as a bit of a derby as well, because of the rivalry between the two teams. I'm really looking forward to playing in one."