The Robins have moved to within five points of safety with two wins on the spin, and Anderson has insisted that the players are "all in it together".
"We are all in it together and we all believe we are good enough. At the start of the season there was never a thought we'd be battling relegation with the squad we've got," Anderson told reporters.
"It is amazing the swings and roundabouts in this league and we are all positive and believe we can get out of it."
Next up for Bristol City is a home clash against Nottingham Forest on Saturday.