Coady impressed on his debut for the north Wales outfit following his switch to the Stok Cae Ras from Leicester City.
The centre-back produced a vital block to prevent Adam Armstrong from scoring in the opening half and ended the contest having blocked three shots and made 10 clearances – both the most of any player on the pitch.
And the 32-year-old feels Wrexham’s performance showed they are more than capable of competing in the Championship following three successive promotions from non-league.
“We know what we are and we know we’re here to upset and disrupt a few teams in this division. We’ll keep building and improving,” he added.
“It’s amazing to see where this club has gone. I have so much respect for what the club have done since the National League to get to this point.
“I think we’re at a point now where we don’t want to just enjoy being here, we want to improve and mix ourselves with teams like this and maybe go higher.
“To do that we have to make sure we’re dominant at this level, and we’ll make sure we get to that level as quickly as we can.”