While he can see an improvement in the team since Pereira took the reins from former manager Gary O'Neil, Goodman admits their immediate fixture list will prove a real test for the Portuguese and his players.
Goodman, who scored 25 goals in 82 appearances for Wolves, told Tribalfootball.com: "The first three games were great under Pereira, where they could take advantage against Leicester City, on a terrible run, followed by Manchester United and Tottenham, who are both in limbo for different reasons at the moment.
"Seven points from those games was a great start; you could safely say that they played all three of those teams at just the right time.
"They've since lost against Forest and Newcastle, but they're in completely different situations to the teams Pereira played at the start of his reign.
"Forest and Newcastle were both on long winning runs at the time. Wolves had a difficult first 10 games at the start of the season, too; the most difficult out of anyone according to Opta.
"Those fixtures are coming round again now, they're right in the middle of them. The next half a dozen games look difficult for them, with Arsenal and Liverpool around the corner after their Monday night loss at Chelsea.
"They'll really have to dig in. It's about hanging in there, but there's definitely been an upturn from what I've seen.
"He's got a bit more buy-in from the supporters; they'd lost four in a row when they sacked Gary O'Neil.
"If they can get through the next few games, they should have a run of matches after that which they can hopefully take advantage of."
Meanwhile, a lot has been made of Pedro Neto's departure from Molineux to Chelsea in August, but Goodman says it's another summer sale which has been felt the most this season.
He continued: "Any team would miss Pedro Neto.
"They sold Max Kilman, too. I think they've missed him more than Neto, because they've conceded 48 goals in 21 Premier League games this season.
"You're going to be bang in trouble if you're letting that many goals in.
"I don't think they'll sell Cunha in this transfer window; the fans would be furious and they would probably revolt."
With Wolves sitting outside the dropzone only on goal difference, Goodman says their chances of survival will get down to a straight shootout with Ipswich Town.
He added, "Most would say Southampton are down, Leicester have just lost seven in a row and it looks tough for them as well. That leaves Wolves in a scrap with Ipswich and Everton for me.
"I know people are saying that Everton, after the win over Spurs, will be safe now under David Moyes, but I don't necessarily see it that way.
"Wolves played Spurs at the right time, and so did Everton last weekend. They still have a bit to do; I wouldn't make it a two-horse race between Wolves and Ipswich just yet.
"Wolves only need to finish above Ipswich or Everton. Hopefully they'll be adding to the squad this month rather than letting someone like Cunha go."
- Don Goodman was speaking to Tribalfootball on behalf of Casino.co.uk