Fans of the Tynecastle club staged protests outside the ground following the 3-2 home defeat to Queen of the South on Saturday, which followed last week's humiliating Scottish Cup exit at the hands of Brora Rangers.
While accepting that the results are unacceptable, Pressley, who played alongside the current Hearts boss for seven seasons in the late 90s and early noughties, says calls for Neilson's removal are over-the-top with the club 10 points clear in the Championship and on the brink of achieving promotion back to the top flight.
"Robbie will completely understand that's not the standard that's expected at a club like Hearts, but also I certainly think there's been an overreaction. There's no doubt about that,” Pressley told Sky Sports.
"When Robbie took the job in the summer I spoke to him personally and I said to him although I totally disagreed with the way that the club was treated and relegated, I thought for him on a personal level it was a blessing in disguise because I don't think the current group of players are good enough to make the sort of impact in the Premier League that would be expected by the Hearts supporters.
"So this year would give him the opportunity to gain promotion gain that credit in the bank and go into next year with momentum. The last couple of performances have probaby taken away that credit in the bank.
"There's going to be a very important summer for Robbie moving forward. I don't think he'll get the time in the Premier League in the eyes of the supporters unless he makes that impact.
"But I think what everyone needs to realise is that for a club like Hearts the recruitment over a period has been pretty poor and it's going to take a good two to three years of stability to really turn that club around."
Pressley also played down the fan unrest and insisted Neilson should be given time to fix the issues at the club.
"I saw the pictures it was 20 or 30 supporters out there. It wasn't significant numbers," he stressed.
"We sometimes read social media and believe that is the opinion of all supporters - it's not. There are many supporters that are understanding of the positon. That's not to say that there's an acceptance of losing to Brora Rangers. No, Robbie like everybody understands that you just can't do that at Hearts. But sometimes these things happen and for me the club has been mismanaged for a period of time and needs stability.
"Of course, when you pick up the reins like Robbie has, you're going to experience some difficult times when you're trying to build. But part of being a good football manager is actually steering the club through these difficult periods.
"Sometimes he must wake up in the morning and think we're 10 points clear and they're still wanting me out. It's an incredible scenario but he's a strong manager, he's a good person, he works exceptionally hard at that job, and there's no doubt he deserves time to turn that club around."