May took Falkirk off the bottom of the SPL just last week for the first time in more than five months when Falkirk secured a rare victory in Aberdeen, but a section of supporters vented their anger towards him on Wednesday night after a 1-0 home loss by Kilmarnock consigned them to the basement again.
Pressley moved on to the coaching staff when May succeeded John Hughes and now finds himself with the task of bridging the three-point gap on Hamilton, whose surprise win at Dundee United lifted them off the bottom.
Pressley, whose first game comes at former club Hearts, told a media conference: "I certainly wouldn't have taken this job if I didn't believe we can stay in the SPL.
"Make no mistake about it, we will stay in the SPL, of that I have no doubt.
"You can dress football management up any way you want but the single most important factor is winning games.
"I intend to bring that to this club. I have a huge belief in the current group of players, my current staff and the board, and my own ability to manage this football club.
"Because of that, we will stay in this division, no doubt about it."
Source: Team Talk