Ospreys face Edinburgh in Bridgend on Saturday, their final game before the international break.
The Swansea-based side are bottom of the United Rugby Championship having won only one of their five games so far this season.
“We are all determined, myself included, to put right what has been a disappointing block for us,” Booth said.
“I am confident that everyone is still on board, still doing what needs to be done. The atmosphere in the room when it’s full of our players is still very determined and very buoyant.
“That tells me that the culture is good because that’s what gets tested in difficult times.”
Ospreys will be without fly-half Dan Edwards (concussion) against Edinburgh but are boosted by the availability of Wales internationals Jac Morgan, Dewi Lake, Adam Beard, Owen Watkin and Gareth Thomas.
“When things aren’t going as you want, and they are not going as we want from a result point of view, people look to your senior players, leaders, to lead by example, create confidence and show the way.
“We’re dropping in four really important leaders and very important players for us.
“We’re obviously hopeful that those things play a greater part than what we had to endure a little bit last week.”