Gerrard brought Davis back to Ibrox in January 2019, and the 36-year-old Northern Ireland midfielder played a key role as they romped to the title unbeaten last season.
But Gerrard has now left the Scottish champions, named as Dean Smith's successor at Villa Park on Thursday.
"Firstly, I thoroughly enjoyed working under him and his staff," said Davis, who added that he had been in touch with Gerrard briefly since the news broke.
"Obviously we've got great memories from last season going unbeaten, it was a great achievement. It's disappointing to see him go, he had a good relationship built there and a good squad of players. Unfortunately that's football.
"I wish him the very best moving forward. He's going to be a top manager and already is."
Davis, who came through the ranks at Villa as a youngster, believes Gerrard will find everything he needs in place at the club.
"It's a fantastic football club," he said. "Obviously they've had a little bit of a disappointing couple of months in terms of results but they've got a good squad of players and they're looking to push up the league."
Former Rangers midfielder Giovanni Van Bronckhorst has emerged as the favourite to take over at Ibrox, with the side four points clear of rivals Celtic at the top of the table.
Reports suggest the Dutchman could be poised to succeed Gerrard this week after ‘positive’ talks were held with Rangers representatives over the weekend.
"Whoever does come in is going to inherit a really strong squad and in a good position at this point in the season with a lot to play for," Davis added. "The goals remain the same."
Before returning to Glasgow, Davis has the small matter of a match against Italy to deal with as the European champions head to Belfast needing victory to be sure of their place at the Qatar World Cup.
During the build-up to the match there has been much focus on Davis' future. He stands to win his 132nd cap in Monday's match, but has said he will then take time to reflect over the winter.
"I've been asked about it quite regularly over the last few months," he said. "I don't know why people are trying to retire me. In all honesty, at this stage in my career I don't think too far ahead.
"We've enough to contend with bringing the European champions here tomorrow. My full focus is on that, and it's important to reflect after the campaign and see how we move forward...
"I just want to enjoy my football and get as much out of it as I can, whether that's club football or internationals. I don't look too far ahead. I certainly haven't made any decision."
Meanwhile, former Aberdeen boss Derek McInnes has revealed he would relish the chance to manage Rangers, but conceded it was unlikely.
"Any manager, including myself, would love that kind of opportunity,” McInnes wrote in his Mail on Sunday column.
“But, as I write this, others look to be leading the running, most notably my old teammate Giovanni van Bronckhorst."