Lansdown said he was well aware that the Robins have a poor record in the play-offs, having failed to win promotion in all four previous attempts.
But he said he did not see it as a problem.
"People will refer to it but this is a different time, a different era - Gary Johnson is not the same manager as we had before.
"He's organised this team, he's organised this football club and we've got a set of players that don't give up.
"They work so hard for each other and we've got a set of fans who have really got behind the club now. We can go a long way together, and that's what's so exciting."
City have been allocated 36,007 tickets for the play-off final and Robins fans will be in the west end of the stadium.
Tickets went on sale at 0900 BST on Thursday to season ticket holders and City Foundation members, with a limit of two tickets per applicant.
Fans can buy tickets on general sale from 0900 BST on Sunday, with a limit of four per applicant.