Motherwell boss McGhee has opted to stay at Fir Park after previously admitting an interest in the vacant Hearts position.
Hearts have resumed their search for a new boss and Berra is keen to see stability at Tynecastle under owner Vladimir Romanov.
"The club wanted Mark McGhee, but he made the decision to stay at Motherwell and all credit to him," said Berra.
"There are other good managers out there who can do a job and hopefully when someone does get appointed they can take the club forward.
"I think it would be good to get a British-style manager who would come in and know what it takes to compete in the SPL.
"But they've got to make the right decision. It's very important that the manager is in place for pre-season because if he is not, then comes in two or three weeks later, then it might be hard to bring in his own style of play."
Berra believes Hearts should have no problem attracting the right calibre of boss and also hopes there will be no mass influx of new faces.
He added: "We are a big club, we have a big fanbase, a nice stadium and an academy.
"We have the potential to be a very big club, but we probably need a manager in place with his own backroom staff who is going to take the club forward and who will improve players individually.
"Whoever comes in will target players and hopefully Mr Romanov will back him and show him the money, but you don't want to be silly and spend too much money.
"It's about quality not quantity now and I think if we bring in a few quality players to the squad, get everyone working in the same direction, then we can be up near the top."