The former Chelsea frontman took over the reigns at Loftus Road in December and has guided the Rs to 11th place in the Championship with eight games remaining.
But having recorded just five league wins under the Dutchman so far, Chery knows that the squad has underperformed and must do better next term to have any shot at promotion.
He said: “There are a lot of good players here; we have international players, but we are mid-table and that’s too low for these players; that’s what myself and the manager thinks.
“I hope it (promotion) will be next season because now the manager has come in, he can also do pre-season, buy new players and decide which players stay or go. I think we’ll be fine for next season."
Chery also had positive words for former boss Chris Ramsey but hailed the appointment of his fellow countryman Hasselbaink.
He added: “Ramsey was also a good manager, but Jimmy has his own stuff that he wants to bring to the place – he makes us like a team which is the biggest difference to the other coaches.
“If some players go, you have to show yourself and make yourself important for the team – you have to train well and when you get a chance in the team you have to play well so the manager cannot change you again."
Having prolonged his stay in the Rangers starting eleven in recent months, former Eredivisie star Chery thinks he has contributed to the team’s current impressive form but admits the chances of reaching the playoffs are few and far between.
“The last few weeks I have played good and also for the team, we have made progress but it is hard to go to the playoffs but you never know – we will see what happens at the end of the season.”
His fledgling partnership with striker Seb Polter is also proving to be a highlight in the final weeks of the season and it is something that Chery attributes to their similar introductions to the game.
“He [Polter] played before in Germany, I played in Holland – it’s very much the same.
“When I play I score goals, that’s what I always say – the fans love me because I score goals - that’s the only thing you have to do, score goals”