The Glovers picked up a point for the goalless draw before the Grecians claimed an additional bonus point for a penalty shootout win.
After Alex Pattison and Omari Patrick missed from the spot for the hosts, Jack Sparkes secured a 4-3 shootout victory to edge the Devon outfit ahead in Southern Group D.
Despite missing a host of chances to claim all three points, Way was left to praise his side’s effort.
“It’s important we look at the positives,” he told iFollow Glovers. “It’s another cleansheet so I can’t have a go at anyone. Alex Pattison was very, very effective and Omari Patrick won us the game on Saturday, so I can’t complain.
“I’ve told them to keep their heads up because they gave everything and we had two or three efforts one-v-one and on a normal day they’ve gone in for us.
“The players kept fighting until the end but we were unfortunate to lose the penalties. I thought the whole team gave absolutely everything so I’m not too disappointed. Having said that, like every game, we wanted to win.”
Despite the penalty disappointment the stalemate in normal time saw the Glovers record a fifth straight cleansheet.
Remaining hard to break down, Way was left to priase the whole team for their defensive resoluteness.
“It’s an amazing effort from the whole team, not just the goalkeeper and back four. It’s a Phenomenal effort from front to back.
“Exeter left four up at times and made a number of effective substitutions but I felt we managed to take them the other way at times and caused them real problems.
“I don’t know how many corners we had but we were unfortunate not to stick the ball in the back of the net.”
Town now head into a 10-day break with Saturday’s league clash with MK Dons postponed due to international commitments.