Vale's third-place finish in League Two last term sealed their return to the third tier of English football following a five-year absence.
While promotion was greeted with great celebration, much of the campaign prior to that point saw fans divided.
Most remained positive and patient, but a vocal section of supporters chose to vent their frustration at the team's failure to win at Vale Park on multiple occasions.
Adams is urging all fans to get behind his players throughout the upcoming campaign, as he feels that their support could prove to be the difference between staying up and going down.
He told the club's official website: "It is not always going to go our way, it didn't always go our way last season.
"But their support, not necessarily when the times are good, but when the times are not so good is going to be important.
"They have got to get behind each and every individual at the club and if they do that, we will hopefully put a side together that they can justifiably be proud of and we will try our best."
Vale begin life back in League One today when they host Brentford at 3pm.