Burton brought their regular campaign to a thrilling conclusion with a 3-2 win against Martin Allen's title-winning side and now take on Bradford in the play-off semi-finals.
Rowett said: "Gillingham have had their moment of glory and hopefully in two weeks' time we'll have ours.
"We've finished with our highest points total by a long way since we came into the Football League and we've finished fourth in the league.
"We've missed out on automatic promotion by not many points. It's been a tremendous achievement so far."
Burton visit Valley Parade on Thursday - less than two weeks after a narrow defeat there ended their automatic promotion hopes - and host the return leg next Sunday.
Rowett said: "The games against Bradford will ultimately be about putting in two excellent performances and making sure we remain as competitive as we have been all season.
"We've been preparing for this for a month, we know what we're doing and we'll be as organised as any team in this competition."