Nine straight losses looked to leave the Ashton Gate side on the verge of relegation to League Two.
But new boss Gary Johnson, who quit Yeovil to replace Brian Tinnion, has engineered four wins and two draws from their last six games ahead of the visit of Scunthorpe on Saturday.
Lansdown said: "I'll give full marks to everyone at the club, panic could have set in but it never did.
"You discover things about yourself in times of adversity and everyone should take a lot of satisfaction from proving to people that we have it in us to scrap and fight for our lives, and play a bit of decent football along the way too!
"Gary should take a lot of credit because he has instilled that work ethic in the players, the all-for-one spirit you need."