As it was the Blues made the long journey home empty handed after quick-fire goals from Ben Williamson and Tom Pope usurped the lead given to Kavanagh's team by Courtney Meppen-Walter's first-half header.
Kavanagh said: "It's a very disappointing result. I can't fault the lads for effort because they gave everything, but it wasn't to be.
"We created the chances to go 2-0 up and we've paid the price for not taking them. Goals change games and change mentalities and when Vale equalised it affected the moral of our players.
"It's a shame because we were in front at half-time and had our tails up. We played well at the start of the second-half, but have conceded a goal on the break and then the course of the game changed.
"We've got a good group of players who give their all and we've now got to dust ourselves down and bounce back. The lads have done that before and I'm sure they can do it again.
"It's going to be a big period for us now because after going to Sheffield United on Wednesday we've got several games against teams who are around us near the bottom."