Kris Boyd and Kevin Thomson has joined Middlesbrough, while Steve Smith, DaMarcus Beasley and Nacho Novo left Ibrox in the summer."Injuries and suspensions that bother me right now, and more than ever before," said 62-year-old Smith.
"In fact, they do worry me most, as I look towards the new season."
Rangers travel to Australia on Tuesday to continue their pre-season training to defend their Scottish Premier League title.
Left-back Papac Sasha unavailable after suffering a knee injury in last weekend friendly against Queen of the South.
And Smith, who in his last season as a manager at Ibrox, is seeking to strengthen his squad before seeking a third league championship.
"We still have a solid foundation for the team, and if one or two may be added that it would be great," he said.
"But when you are running with a small squad it's the number of injuries and suspensions that hit you harder.
"You have to factor in European football, and not inferior to some of the boys will play with their national sides in the first half of the season. I can only hope that does not accept his sacrifice.
"There is no doubt that may hinder us a little bit in terms of success."
Rangers manager added: "We simply must do everything we can to make sure that everything remains as a reflection, but we must have a certain level of discipline in our game."
Striker Andrius Velická will miss the Australian tour, as he battles back from knee injury which left him in the side since last August.
