The Tynecastle boss has come under fire in recent weeks with defeats to Brora Rangers and Queen of the South bringing fans’ frustrations and concerns to the fore.
The Championship league leaders got back to winning ways on Friday night with a thumping 6-0 win over Alloa Athletic, moving them to within two points of the title.
Pressley had sought to defend his former team-mate during the week, criticising the leadership of the club.
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How the Hearts players rated in the draw against Hibs
How the Hibs players rated in the derby draw with Hearts
Ahead of the match against Alloa, the former Scotland defender, who was part of the punditry team, expressed his view that Ann Budge and Craig Levein failed to progress “a very good vision” and create an “elite environment” leaving Neilson to “pick up the pieces”.
He said: "I think the one thing we must consider is that when Craig and Ann came in seven years ago they put in place what I consider to be a very good vision and strategy for this club moving forward.
"The one problem was they didn't fill the appropriate places within the club with the right people. People that would challenge, and people that would create an elite environment.
"Over the past couple of years I think it's been neglected and now we find that Robbie is in a situation where he is going to have to pick up the pieces.
"He is going to have to start again, and this is going to be a big, big summer for Robbie. A big summer for Joe Savage.
"But, in my opinion, he definitely needs the backing of the Hearts support."