Gregory has seen his side slide down the Premiership table during a run of eight games without a win. Tonight they face Southampton at Villa Park in the Worthington Cup in a match that the home side can ill afford to lose.
Doug Ellis, the Villa chairman, is giving Gregory time to put things right, but a win is essential in a competition that offers the prize of European qualification.
Harrison said that Gregory has remained in an upbeat mood through his team's indifferent run. "John is coping with the pressure very well and with a lot of dignity," Harrison said. "The pressure is there for all to see, and we are under no illusions as to what is expected of a high- profile club like Aston Villa.
"However, John is very positive and remains very positive in the dressing- room. Everyone is human, and I am sure he has his reflective moments about the current position. I'm sure he is suffering inside.
"But he doesn't show it. We all try to stick together and keep buoyant, but he has taken a lead himself in ensuring that is the case - and I can say that with my hand on my heart.
"If we could say exactly what had gone wrong then we would make sure it didn't happen. But at any club these situations arise, and even the great managers down the years have all been through it.
"We've not yet put it right. But the signs were good against Everton on Saturday, and the players wanted to do it for John Gregory. The performance wasn't pretty or fluent but it was hard-working and motivated.
"They wanted to win. They wanted to win for John Gregory - and that reflects the mood of the camp. In similar situations in the past I have seen dressing-rooms that have been flat and defeated. That is not the case here.
"John will come through this - and full credit to the chairman for giving him time to do that - and he will come through it a better manager."
Gregory did not attend a pre-match press conference for the second game running, although on this occasion Harrison reported that he was suffering from influenza.
Villa are facing a vital period in which they can turn their season around with successive home games against Southampton, Newcastle and Sheffield Wednesday in the Premiership and the wild-card losers in the FA Cup.
Gregory's team will be seeking revenge tonight for the league defeat by Southampton in their last home match three and a half weeks ago. Gregory is likely to name an unchanged side. Ugo Ehiogu and Darius Vassell are injured, while Benito Carbone is cup-tied.
The game is not attracting great interest from Villa fans, with only 13,000 tickets sold up until yesterday despite a reduction in prices. A final gate of around 16,000 is expected in what is the first of six possible home games for Villa before the new year.Reuse content