And the draw for the next round was made on Wednesday afternoon and Wrexham now know they will face National League counterparts Solihull Moors away if the Moors overcome Rangers Colts on October 29.
"It's a good mix [of teams]," Keates said after he got his first win since returning to Wrexham against St Mirren Colts on Saturday.
"It's a competition I want to show respect to but I used the game to get minutes into some of the players."
When asked whether he was targeting the competition as a realistic chance of silverware, Keates said: "As long as we don't end up travelling to Inverness in the next round we do.
"We want to win football games because winning football games breeds confidence. [Saturday's win] was another building block."
Scottish Challenge Cup quarter-final draw:
Solihull Moors or Rangers Colts v Wrexham
Ties to be played on the weekend of November 16/17.