The Mariners secured a third consecutive promotion on Tuesday with a 3-0 win over Glossop North End.
Should other results go their way, a victory at Skelmersdale United tomorrow could secure the Evo-Stik North Division championship.
That would make it three league titles in as many years for the Mariners, and joint manager Picton will not be satisfied until that is sealed.
He said: “In the last four games, all of the players have got to show with their performances – and I’m sure they will – that they’re fully committed and ready to take on the next challenge at this club, and that they want to be a massive part of that next season.
“We’re looking for players that have got that mentality, who don’t take their foot off the gas because we’ve achieved one goal this season.
“They have to want to make this season not just a really good one, but another special one for us.
“The only way we’re going to do that is by winning the title and doing it in style.
“We’ll give ourselves a pat on the back for winning promotion, but we’ll hold back the real celebrations hopefully for when we lift that trophy.”
Shields will win the title tomorrow should they secure three points and nearest challengers Scarborough Athletic fail to win at eighth-placed Colne.
Whatever happens in their next four games, the Mariners can prepare for life in the Evo-Stik Premier Division next season.
Picton says preparations are already being made.
He added: “We’ve made tentative plans about next season already, but now they’ll have to be concreted, because we know exactly where we’re going to be.
“We’re massively looking forward to that next level of challenge, and the players have got to relish that as well.”
Shields are without Anthony Callaghan going into tomorrow’s game, and Barrie Smith is a doubt.
The match will be held at Prescot Cables’ Volair Park (L34 6HD) due to a ground-share agreement.
A win would guarantee the Mariners’ place in the top two at the very least.