The Bucks edged a well-contested Greenfields friendly 1-0 thanks to a 14th-minute winner from new forward Tyrell Hamilton.
But Drayton, who lost the warm-up game 6-1 last season, stayed in the contest throughout and would have been decent value for a draw, although Telford could have won by a bigger margin late on.
“It was important we showed a good mentality, which I thought we did, and everybody is healthy,” said Cowan, whose side have won their two friendlies so far by the odd goal ahead of the visit of Shrewsbury Town tomorrow.
“We look very rusty, with the centre-halves’ timing and things like that, but outside of that I’m really happy. Credit to Market Drayton, they are brilliant hosts and have been class today.
“I thought they were excellent, very competitive. That’s not me patronising them, I thought they showed lots of quality and endeavour as well.
“It was a perfect pre-season game for us.”
Cowan used a trialist at centre-half, on the right of his back three, and is looking to make a signing there in the coming days and weeks. Trialists were also brought from the bench in either wing-back positions.
For Richard Brown’s step four Drayton, going into the first full season under the new boss, the exercise highlighted their progress as they prepare for the Northern Premier League First Division West campaign.
Drayton competed well and used the ball intelligently, particular after the break, where they forced a couple of presentable shooting chances.
Brown retained ‘seven or eight’ members of his squad from last season. New acquisitions include Reece Jakobs, Reece Taylor, Jakob Burroughs and Liam Riley-Stewart, most of whom have stepped up from divisions below.
He said: “I’m very pleased with that, against a team two steps higher than ourselves. We just had to try to match them for fitness.
“We’re never going to match them for ability, that’s not saying our lads can’t play there, but you’ve got to prove you’re good enough – and I hope Gav feels the same, I think we gave them a good game.”
“I think we deserved a draw personally, I know they made a lot of changes and we didn’t, and our lads got tired. But we stuck to the task.”