Paynter stepped up after Dave Wild was relieved of his duties earlier this week, for what the club have described as “a matter of gross misconduct”.
Paynter will be assisted by Jamie Rainford, and his first game in charge of Linnets will be away at Kidsgrove Athletic this weekend.
"I'm okay and looking forward to Saturday,” he said.
“I spoke to the players before, and the main focus is Kidsgrove away. It's been a mad 24 hours. We addressed the players and let them know the situation.
“They've got us to fifth in the table - it's down to them, and it's always been about them.
"We back them and trust them, and we're preparing for a tough test on Saturday. Kidsgrove are strong at home and will be trying to close the gap to us, but if we win, we can really finish off their play-off push.”
Linnets currently occupy the final play-off spot in the Pitching In NPL West Division with five games left to play.
A win on Saturday could see them leapfrog Clitheroe in fourth, while defeat would see them drop out of the top five, should Witton Albion claim maximum points at home to Skelmersdale United.
On whether the approach of the team will change following his appointment, Paynter added: "I've said to the lads, I won't change. I've given them all of my time and energy this season.
"The style of play, we will see. I have a few ideas. A few personnel changes too, maybe.”
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