The Bucks headed to North Street having not played for a fortnight due to a Covid-19 outbreak.
But they were unable to stand up to the physical threat posed by Alfreton, who ran out comfortable winners.
Telford were without some key players for the game while boss Cowan revealed a couple of squad members were struggling with a bug in the build-up to the game.
But he still didn’t hold back when assessing his team’s performance.
“We had some spells in the game where if we had managed to convert our chances it could have been a different story,” he said.
“But ultimately it was a deserved defeat – we were totally outpowered and bullied by an Alfreton side who we just couldn’t stand up to on the day.
“I don’t want to put blame on to the players.
“The bit I can’t do for them is going out there and having the desire to stand up to such a barrage.
“A couple of the things we had worked on, stopping things at source, we weren’t able to do.
“It was a deserved defeat. We weren’t anywhere near where we expect to be.
“I’m disappointed for the travelling supporters, they had waited two weeks as well.
“I don’t want to be too critical because the group is depleted.
“But if we were passed off the park you would accept it.
“But Alfreton played to their strengths and I didn’t feel we had the desire to stand up to that.”