Nancekivell, appointed in the wake of Carl Fletcher's sacking, was left to rue the dismissal of striker Nick Chadwick, which came just moments after Jennison Myrie-Williams had handed the high-flying hosts a 32nd-minute lead.
He said: "I thought we started brightly and the players put into practice what we were working on in the week.
"The sending-off changed the game. I genuinely didn't see the incident myself but if Nick is guilty he will be punished.
"It made things very difficult after that. Port Vale have got a big pitch, quick wide players and matchwinners in the penalty area, so it became tough.
"We were disappointed with the second goal. I felt if we could have hung in there for 25 minutes of the second half we would have got a chance or two, but it wasn't to be.
"There is no problem at all with the spirit of the players. They are a good group of guys who care passionately about the club.
"The lads are hurting at the moment, but I couldn't fault the attitude or application of any of them and I know they will pick themselves up and go again.
"I sensed a real togetherness in the dressing room and when you have got that you have always got a chance."