The Rockets were the surprise package during the 2023/24 campaign, securing sixth place even after selling at least seven key players before the season kicked off.
Until recently, Beganovic, who succeeded Ramovic in November last year, had masterminded an 11-game unbeaten run in the league, but following two successive losses, including a 4-1 drubbing by Mamelodi Sundowns, Beganovic is circumspect.
"Last season we needed a draw in the last game to reach the top four, but we lost 1-0 to Polokwane [City] – I remember that game, it was in Polokwane," said Beganovic.
"But this season, it's tough for me to talk because we started [winning] after six games, and then we fought and we only tried to win some games so that we're not at the bottom [of the log].
"But, also in the beginning, when I came in as head coach, I said I believe in this club and I believe in this squad because I know what a quality group of players we have.
"And I can't imagine we can reach between 10th and eighth position, if we just work like we worked [during our unbeaten run]."
Galaxy were contenders for the early relegation dogfight prior to Ramovic stepping down, and the Bosnian tactician believes their form since then allows him to dream.
"Inside, yes, I want to reach something better than last season because I want to see progression everyday, it's simply me – if I want to be in the same place or level every year, something is wrong with me," he added.
"I want to see progression, I want to see how players improve and I also want to see how my coaching staff improve, and everybody at the club.
"We need to grow, we need to improve and try to put our goals higher, and then push to try to reach those goals, even if we don't reach that goal and we fall a little bit short, it's also good for us."