It is just 38 days since Pereira signed a new three-year contract and sources have told BBC Sport he is not in immediate danger.
Shi and those in charge still feel his experience will be crucial in the survival battle, having taken them from second bottom to safety last season. Although, predecessor O’Neil signed a four-year deal on the eve of last season and only lasted another four months.
Domenico Teti’s arrival as director of professional football in the summer is also a sign of the position of strength Pereira held at the end of last season, the pair having worked together in Saudi Arabia at Al-Shabab.
There is a hesitancy to change given the amount of managers the club have gone through recently and fan reaction will not sway Shi.
The fact Wolves stayed up after failing to win any of the opening 10 games in 2024-25 shows it can be done again, although it is six months since their last Premier League win.
“It’s normal in football, if we win two or three games in a row everything changes,” said Pereira in his post-match press conference.
“Two months ago they sing my name because of the work we did last season [means] we are competing in the Premier League and not in the Championship. Now they sing my name maybe to sack me.
“I’m not worried [about his job], it’s not about me. It’s about the team, the players. My work is to help them to come again, to be mentally strong for the next fight.”
Pereira also tried to diffuse any tension with supporters, revealing what he said to the revolting fans.
“What I said to them is we work a lot and we need to fight together,” he said.
“I understand the frustration. When you are there for 90 minutes trying to help the team and the team gave everything on the pitch to win but, in the end, you concede a goal, I understand the frustration.
“What I must say to them is if we fight with them, united, we can win games. If not, without them, it’s impossible.”
The tipping point for Pereira would come if he loses the faith and confidence of the players, which he has not done.
There is an acceptance at Molineux results have not been good enough but the performance on Sunday as they fought back from 2-0 down, despite defeat, reinforced the players remain behind the manager.
“Yes, of course, all of us are,” said striker Jorgen Strand Larsen.
“We know what we did last season. We’re not blaming anyone here. Obviously, it’s tough for a team with a lot of changes in the summer.
“There are a loads of new faces and it needs time to adapt. That’s why I’m feel like in the last few games we’re getting there.”