Vale manager Martin Foyle said he would have settled for a point before the start but was bitterly disappointed not to get all three.
Vale reached the 90-minute mark 2-1 to the good, but their hopes of lasting out five minutes with added time were dashed when referee Phil Prosser spotted a handball as they defended a corner.
"It was clearly a Port Vale hand that flipped the ball away from the head of the Hull player Leon Cort although I don't know which player," Taylor added.
Vale attacked from the start and soon took the lead when Lee Matthews showed great vision to beat Boaz Myhilll from nearly 30 yards, the Hull defence looking like strangers in the early stages as the visitors continued to force the pace.
Cort however put Hull back in the picture when he headed the equaliser from Andy Dawson's free-kick.
In the second half Hull set out to claim their expected victory, but the Vale defence, with George Pilkington and Sam Collins in outstanding form, proved unyielding.
Vale took the lead again when the outstanding Billy Paynter's cross was headed into his own goal by Damien Delaney. Delaney, racing back to try to cut out the danger, had no choice but to go for the ball and it ended disastrously for him.
Taylor admitted: "I wasn't really happy with our display over the 90 minutes.
"They are times when you've got to dig in and this was one of those times. It was a very important point for us with Tranmere drawing."
Vale boss Foyle added: "We now gone four unbeaten and are starting to get a little run going.
"I think that we were much the better side, but Peter Taylor knows what it takes to get a team out of this division."