Goals from Joel Kettle and Nathan Hayward either side of half-time sealed defeat for the Robins.
It left Carruthers rueing a missed opportunity.
“I’m very disappointed,” he said. “I am not a good loser, I hate losing football matches and I thought the game was there for the taking.
“We have been done by two set-pieces. We huffed and puffed but, in all honesty, we didn't have any desire or energy.
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“The only good thing is that you learn about players, pitches and situations.
“There are the kind of pitches we will have to deal with in the winter.
“We will have to play direct football, to play the percentages and not take risks. You can’t get the ball down and play.
“We had too many not at the races today.”
Attention now turns to the home match with Corby on Saturday, with Carruthers eager to return to winning ways.
“We have had Corby watched and we will assess their last game,” he said. “We want to get back to winning ways. The league is our only focus now, so that could be a blessing in disguise.
“It is time to regroup and recharge. It can be a wake up call for our away games.”
Alex Troke and Ollie Brown-Hill had chances for the visitors inside the opening 15 minutes.
But they fell behind when Kettle headed home from close range on 36 minutes.
Bromsgrove doubled their lead through a Hayward header on 49 minutes.