Shrews striker Dave Hibbert charged down goalkeeper Scott Brown's attempted clearance to level the match in the 72nd minute after veteran striker Barry Hayles had fired Cheltenham into the lead after an hour.
And Brown then failed to grasp Hibbert's header from Lewis Neal's cross two minutes later, allowing Joss Labadie to stab in the winner.
"It is a bitter pill to swallow because it was the first time we have played well at home this season," Allen said. "It's hard to take when you lose a game like that when we had the majority of possession and been in the final third so many times.
"We have played a lot worse and won and there have been games when we have been hanging on, but Shrewsbury are one of the best teams in this division and we have outplayed them."
Allen was also quick to defend Brown, who was at fault for both Shrewsbury goals. He said: "The lad is very upset in there and he has done really well for us. It's a steep learning curve and it is harsh when errors like that happen."