City slumped to their lowest league position since 1959 following their 0-0 home draw with Oldham last weekend.
They then parted company with managing director Chris Anderson on Monday.
"With all the off-field stuff that's happening around I do try to cocoon ourselves from it," Mowbray told BBC Coventry & Warwickshire.
"I live it every day and have done since I came here, which is only 18 months ago. Does it filter through to the players? No, I don't think so.
"The key is just to keep working hard and try to enjoy each other's company on the training ground."
City have only conceded eight goals in as many league games this season, but have only scored three themselves prior to Saturday's trip to Gillingham.
"Our form is certainly not scintillating by any standards," said Mowbray. "It's a totally different team, 11 new players, two re-signings.
"But we can't just keep getting the same results just by picking the same players. I've told them there will be changes.
"Having said that, we're not far away from being a good team in this league and we pretty quickly have to turn draws into victories."
Anderson's departure comes as two fan bodies, the Preservation Group and the Sky Blue Trust, have issued statements registering their disaffection with the club's owners, Otium, formerly known as Sisu.
And the local newspaper, the Coventry Telegraph, has been banned by the club for initiating a petition demanding the owners' removal after nine years in charge.
"It's a difficult situation if you put a foot in either camp," said Mowbray. "I don't see myself as a politician-type of manager. I like to get my boots on and try to make us better on the training pitch.
"Things will resolve themselves at some stage. There could be better days around the corner. But, while people move on, the only thing that stays constant is the fans.
"Somewhere along the line, this team will gel, click into gear and then off we go. But we need to have everyone pulling in the right direction."
Coventry City manager Tony Mowbray has said the struggling Sky Blues have to pull together following a bad week for League One's bottom club.