Anthony Elding scored either side of substitute Sean Rigg's goal for the Valiants as the visitors claimed a win that keeps their slim survival hopes alive.
But Grew, whose side missed out on the chance to go joint seventh, was furious with his side.
"I've just come out with a few home truths in the dressing room. Some of the players don't like it, but that's tough," he said. "Our trouble is we don't have enough characters and leaders when things are going against us.
"Why we allowed Stockport to dictate the pace from the start of the game is a mystery to me. It was a massive game, we were at home and we should have been up and at them. I had a go at them at half-time and there was a big improvement. If Sean Rigg had scored when he went through we would have won the game, but instead we've contrived to lose it."
Angry Vale fans staged a demonstration against the club's board after the game and Grew added: "Of course I can understand their reaction. I can only concentrate on what happens on the pitch, but things haven't been going well and the fans pay their money and care about Port Vale."
Source: PA
Source: PA