The Robins are looking for their third straight victory at Ashton Gate this Saturday when Sean O'Driscoll's former side Nottingham Forest are the visitors.
Wins over Ipswich and Watford have helped City climb to within five points of safety and Anderson, who has started all four of the new manager's matches in charge, says they can secure npower Championship football for another season.
"We are all in it together and we all believe we are good enough," he said. "At the start of the season there was never a thought we'd be battling relegation with the squad we've got.
"It is amazing the swings and roundabouts in this league and we are all positive and believe we can get out of it."
O'Driscoll spoke about the emphasis he has put on 'the boring things' after back-to-back home wins and Anderson echoes his manager's views that they are working on getting the basics right.
"We are more organised now," he said. "We are together and we are working hard. We are keeping it easy and keeping it simple. You have to go back to basics sometimes and don't complicate it."