Luke Summerfield's header on the stroke of half-time earned relieved Shrewsbury only a fourth win of the season, with the three points enough to lift Graham Turner's men out of the League One relegation zone.
But Davis was left bitterly disappointed that his side's strong penalty appeals shortly before the goal were rejected, on-loan Fulham striker Lauri Dalla Valle appearing to be barged over in a congested area.
"I felt we should have had a penalty," Davis said. "It was an absolute stonewaller. You won't get any more stonewall than that and it was just five minutes before they scored.
"That should have been given and I spoke to the referee about it and he said it wasn't. Everybody else in the ground thought it was apart from him."