With the Robins chasing shadows, the visitors led 3-0 at the break thanks to Danny Stevens goals either side of an Elliott Benyon header.
The Devon club could even afford to miss a Nicky Wroe penalty in the opening minute of the second half but were finally forced to weather a late Cheltenham storm that saw Josh Low pull a goal back after 55 minutes.
"If I am brutally honest, the first half was absolutely diabolical," said Allen. "Players who have trained hard and been given an opportunity to be professional footballers have let themselves down, let me down and let the club down.
"It was a shocking first-half performance. If you let people pass the ball around in pretty patterns, then don't tackle them when they are going to shoot, then you will lose the game.
"We were found wanting big style - and it's not good enough for me and the club, so I will have to do something about it. Some people are playing for their careers and it's not good enough. The crowd were right to boo them off at half-time as they have paid good money to watch that and they deserved a lot better."