Experienced striker Tom Pope netted a first-half opener for the Valiants before Otis Khan restored parity and completed the scoring on 66 minutes.
The Glovers are unbeaten in their five Sky Bet League Two home matches so far and although the sequence pleases Way, he admits he wants more.
“The players gave everything, certainly towards the end,” he said.
“We have new young players who will take time to adapt and develop, and need all the support they can.
“Matt Worthington came in at right-back and his effort was second to none.
“It’s another point and we have a good home record but we want more, and so do the supporters.
“We knew Port Vale would come and give it everything as you always expect a reaction when a team has changed manager but overall we should have won.
“Every team is searching for that winning solution and we have to come up with one that gets us the points at Chesterfield on Tuesday.”
Daniel Alfei was forced off after just 10 minutes and will be assessed ahead of the trip to the Proact Stadium.