The Robins are struggling at the bottom of League One, having lost their last seven games in all competitions.
This despite former manager Brian Tinnion quitting the club, and former Latvia boss Gary Johnson arriving from Yeovil Town.
Speaking at the club's AGM, Lansdown said: "I take full responsibility for the League position and the financial state we are in.
"As chairman, I can't hold my head up high and say I've done a good job.
"We need to get into a situation where the football club and the stadium company are, at the very worst, breaking even."