Saydee has netted two goals in two starts since joining for the season from Premier League Bournemouth, including the opener in Saturday’s 2-1 win over Burton.
But Cotterill claims the 20-year-old is still some way short of peak fitness and will keep pushing him hard.
He said: “I did say to Christian two in two is not good enough. When he gets 20 in 20, then he will get a well done.
“Let’s see how he goes. We will keep him going and get him up to speed. There are still some things he needs to work on in his game.
“But it was a brilliant goal. He showed strength, power and pace and he is almost undefendable at times.
“But he has to keep that going. We have to make sure we keep the hammer down on him and make sure he is fit and even sharper.”
Cotterill had called for his forward line to start delivering prior to Saturday’s game and was rewarded with Town’s most clinical performance of the campaign so far, the two goals coming from their only shots on target.
Substitute Ryan Bowman got the winner after Victor Adeboyejo had levelled for the Brewers but the boss still wants more.
He said: “The forwards haven’t been firing enough. I still think we need more from them, even with two strikers scoring on Saturday.
“What we need is to have them fit and firing all the time. It is not just about scoring. You can go on and be really poor and score a goal and get away with it. You won’t get away with it here.
“They need to do more in free play because you won’t always get a chance like you did on Saturday.”
Cotterill is confident Marko Marosi will be fit for Saturday’s trip to Cheltenham after the goalkeeper played through the pain barrier to help his team to victory.
The 28-year-old cut his hand and dislocated a finger making a save early in the second half but stayed on and preserved the victory with a brilliant stop to deny Sam Winnall late on.
“I thought he was magnificent,” said Cotterill.