A 16th-minute penalty from Sam Baldock was enough to beat an off-key Saddlers side, who rarely tested home goalkeeper Elliott Parish, as City secured only their third league win of the season.
Cotterill said: "We are making small steps in the right direction, but I still regard any results we get before the January transfer window as a bonus.
"There will be changes then, as well as a lot more hard work. We made life difficult for ourselves by not taking our chances, but it was an excellent clean sheet against a very good side.
"We lost Bobby Reid with an impact injury to his lower leg and it is too early to say how serious it is.
"We have created chances in every game since I took charge and need to convert a higher percentage.
"But you have to keep getting into positions to score and Sam Baldock is doing exactly that."
The deadlock was broken when City midfielder Bobby Reid was tripped by Saddlers goalkeeper Richard O'Donnell as he burst into the box on the left.
Baldock found the middle of the goal with a drilled spot-kick and might have gone on to score four or five.
Reid had to be replaced because of injury after 27 minutes, but the home side stayed in control and could have been out of sight by the break as Baldock squandered two great chances.
Walsall were restricted to long-range efforts in the first half and went close just before the interval when Romaine Sawyers fired narrowly wide from the edge of the box.
The visitors lifted their game in the second half, but were still unable to force a testing save from Parish.
At the other end Baldock had two more chances to make the game safe, but on each occasion was denied by goalkeeper O'Donnell.