The Tractor Boys were beaten 4-2 on penalties by the League Two side on Tuesday night, after a 1-1 draw in normal time at St James Park.
Hurst was left unhappy with his side's attitude against the Grecians and criticised the lack of effort given by the Championship outfit.
"I was disappointed with the performance in both halves. We can pretend we passed it at times and I think we had a couple more efforts second half than we did in the first but it was too slow, too pedestrian and people not really playing the way they were supposed to and not making it as fluid as it needed to be," Hurst told the Ipswich Star.
"I didn't think we worked hard enough in possession or out of possession. The players will be shown Exeter players running past ours far too easily and I'm not having that they are faster, fitter or stronger. They will be shown things I don't want to see again. There need to be a few home truths. I've said what I am and I'm honest, I say what I think and what I say. And that's what I saw.
"I'm a big believer in that it's about what goes on between your ears and how you approach things. Clearly our attitude wasn't right tonight. There are some massive games on front of us which, while some will say they're good games for us, if we play like that they won't be that's for sure.
"It starts at training and we'll see now who wants to step up and be the type of character that we need going forward. A lot of questions need answering from tonight."
Ipswich next play Championship rivals Aston Villa on Saturday, having gained just one point from their first two matches of the season.