Two strikes from Dom McHale put the visitors in the ascendency and after Avenue struck back through Lewis Knight, the Bucks held on for the three points.
“We put in a phenomenal performance in the first half, and we were well in control,” Cowan said.
“We probably should have been a few goals better off, but then unfortunately just before half-time Jack Byrne passed the ball off and felt his hamstring.
“So it’s another injury to the list. Ultimately, we’ve shown a bit of indiscipline towards the start of the second half and then it was backs to the wall, somewhat.”
With Byrne going off injured and Andy Bond receiving his marching orders for two yellow cards, Telford now have greater concerns on the number of players available.
“We were light from the start,” Cowan added.
“People have got to appreciate that we’ve got some significant injuries going on, and we’re not talking about young lads, we’re talking about big, big players for our football club.
“We’ve five first-team players who are injured and now we’re going to have Bondy suspended.”
McHale, who has four goals in as many games from midfield, has impressed this season and Cowan believes he is getting the best out of him.
“Dom’s got some catching up to do in terms of his career,” Cowan said.
“He’s had a lot of football clubs, as he keeps being told, but I think it’s a similar sort of situation to Brendon Daniels.
“I think people haven’t got the best out of them, so they cast them aside, but I always think if you can’t get the best out of them that’s a reflection of you, and would be more a reflection of my inability to get the best out of them.
“I think what they value is honesty. I’m honest with my players.”