The Norwegian came under pressure early in the season after a poor run of form that saw them go into their meeting with bitter rivals Liverpool on 20 October just two points above the relegation zone.
However, United put in a good performance to draw 1-1 in that game and have since won three on the trot.
The Reds beat Partizan in the Europa League, Norwich City in the Premier League and Chelsea in the Carabao Cup and face Bournemouth away this weekend.
But, looking back on the build-up to their clash with Jurgen Klopp’s league leaders, Neville admitted he feared the worse for his former team-mate.
“As a United fan, I went into the Liverpool game panicking,” he told talkSPORT.
“I was thinking this could be a bad day, this could get moody in the stadium, Liverpool are a great team and they could go 3-0 up – but United played really well.
“Ole had been questioned tactically but he got it right on the day and that was the start of this little run they’re on, beating Partizan and then the Norwich win was big.
“I don’t think they would have been capable of going to Norwich and winning pre the international break. That Liverpool game gave them a little bit of confidence to think: ‘We’re better than this, let’s be positive and beat Norwich’.
“So there has been a mini-revival, but I don’t think Ole will be sat comfortable in his chair. I think he realises he is one game away from the clouds circling again.
“Ole is looking up the table rather than look down, so it’s an important game.”
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