Falkirk threw men forward at Rugby Park on Saturday in a bid to snatch the victory they required to stay up and send Kilmarnock down but Ryan Flynn missed the best chance of the goalless encounter when he volleyed over from 10 yards in the 88th minute.
Pressley had always insisted Falkirk would not go down but he has impressed chairman Martin Ritchie enough to be given the chance to lead the club back to the SPL.
Ritchie said: "The board are really behind Steven and the team, they put everything into it. Steven came in and gave the whole club a lift.
"The club have asked Steven if he will stay on as head coach going into the new season."
Pressley will now look to sort out his future in the coming days.
"I have loved the job," he said. "Obviously there are a couple of things we need to discuss but I have thoroughly enjoyed this job and hopefully we can get things sorted out in the next couple of days."
An emotional Pressley added: "I have said time and time again that this group of players have given me everything since I took over.
"We came up a little bit short but certainly not on desire, commitment and effort. I have nothing but praise for the players.
"It was an emotional dressing room, there were tears in there, we are a very, very close team."
Pressley bristled with anger when reminded of his guarantees of survival during his introductory press conference.
He said: "When I made that statement, what was the worst-case scenario? I have got a bit of egg on my face, big deal. My ego is dented, big deal.
"The most important thing is the football club, not my ego, not Steven Pressley. It's about my players, these supporters and the club.
"I'm big enough and strong enough to take a little slap around the ears."
Pressley has seen his relations with Kilmarnock boss Jimmy Calderwood and St Mirren manager Gus MacPherson strained throughout the relegation battle, but he insists there has been an overreaction to his public utterances.
"I have never personally criticised anyone," he said. "Let's enjoy it a bit, let's relax, let's enjoy the positives."
A relieved Calderwood was less sure about his future after finding it difficult to get through his first relegation battle.
The Kilmarnock boss, who took over from Jim Jefferies on a short-term basis in January, will seek assurances from chairman Michael Johnston over next season's playing budget before committing himself after struggling with the emotions involved in a "nerve-wracking" finale.
"It was absolutely horrible," he said. "It was horrendous, I never want to go through it again. I'm glad it's finished.
"But you have got no divine right and it was our own stupid fault for getting involved in the first place.
"I have not seen the chairman yet, he might be hiding from me.
"I will see what the plans are, I wouldn't like to go through much more of this.
"If the plans are they want to get into the top six, then that's different.
"But if it's just survival then I'll see you at Christmas time or something."
Striker Kevin Kyle may yet stay on at Rugby Park after being moved by the post-match celebrations when thousands of Killie fans invaded the pitch.
The Aberdeen target, who has not yet been offered a new contract, had hinted in midweek he would definitely move on.
But he said: "I have never experienced that before. It was great seeing grown men crying and the relief on their faces.
"It's incredible what a game of football can do to people. I was just glad to be part of it and I'll see what happens.
"If it is my last game, it's good that I have done a fairly good job.
"I have thoroughly enjoyed my time here - the ups and downs, the arguments with the chairman, I got Jim a great job at Hearts!"