Town were at their clinical best in the second half with goals from Francois Zoko, Shayon Harrison – his first professional goal – and Alex Lacey looking to have given the Glovers a convincing victory at St James Park.
But Exeter astonishingly battled back to earn an unlikely point through David Wheeler’s 88th-minute volley and two injury-time strikes from Troy Brown and former Yeovil forward Reuben Reid.
“It shouldn’t happen,” Way told YTFC’s official YouTube channel.
“You’ve got to allow for mistakes but not mistakes like that in the space of five minutes. For it to happen and develop like that, I’m very disappointed and so are the players.
“You’ve got to be strong and resilient enough, and have the knowledge at 3-0 up that even if one goal goes in, you have to take care of it and manage the game.
“After the first goal, I looked at our body language and it took us a long time to get up and we looked deflated.
“If I could’ve made six changes just by looking at their body language I probably would have.
“With goals going in in quick succession, the players have to take responsibility about the way we should have managed the game.”
He added: “At 3-0 up, we were almost over-celebrating. We could’ve scored two goals after that. With Jean’s (Akpa Akpro) chances it could have been four – it could have been five.
“There’s been teams that have come to Exeter who have struggled to get the ball down and play. We did that, certainly in the second half but unfortunately we didn’t manage the last five minutes. I’ll address that and find out why that happened.
“What I have to do is go back over those goals and make sure that doesn’t happen again.”
Town welcome Carlisle United to Huish Park on Saturday, April 1st (3pm).
Tickets for the match can be purchased in person at the ticket office, online or by phone on 01935 847888.