Manager Mark Warburton says that individual accolades are a reflection of Rangers' progress this season.
Warburton is the Ladbrokes Championship manager of the month for August, while full-back James Tavernier received the player's award.
"Any reward we receive as players or staff is for the team," said Warburton.
"We talk to the players and it's about getting rewards for their work and commitment. Anything we get is testament to their endeavours."
Warburton also believes the inquest held by the players following Saturday's 3-0 victory over Livingston showed the squad's attitude and character.
"The reaction to Saturday's result was really pleasing," he explained. "They were unhappy, there were some areas we fell short in and to have that kind of inquest after a victory was really pleasing for us.
"We know the standards we have to set and if we fall short of them then we'll get hurt. We didn't train as well for one day last week and that was reflected in the performance.
"You have to make sure the environment is right for the players to keep moving forward. There are certain tools you can use but it's about the quality of the group.
"The most successful teams are the ones with that consistency, desire and hunger over a longer period. We have to try to match that and hopefully achieve what we want to achieve."
Warburton revealed that work has already begun on identifying potential signing targets for the January transfer window.
But the Ibrox manager continues to sidestep questions about how long his side can maintain their 100% record, and insists that next Tuesday's Scottish League Cup tie against St Johnstone will not be discussed until after Saturday's encounter with Dumbarton.
"From our point of view, it has to be about the league," he said.
Tavernier says that after a period spent on loan at various clubs in England, he has settled quickly into life in Glasgow.
The former Newcastle United defender has scored six goals already this season, a run that has endeared him to the Ibrox support, and although he has ambitions to play in the English top-flight at some stage in his career, he has targets to achieve at Rangers first.
"I feel at home here, I love the fans, the club, how we play, the boys are great," Tavernier said the full-back. "I've really settled in.
"I want to put this club where it belongs and we want to play in Europe.
"[The English Premiership] is he best league in the world, the top players play in the league and that's something I'd like to do in my career, but I'm loving the football here and I'm happy to stay as long as possible.
"It wasn't the score line [that promoted last Saturday's dressing room inquest], we didn't play as well as we normally do.
"We set high standards and we've got to keep them. We need to learn the lesson from Saturday. If the players are reacting to it, you've got a great group of lads. That will make us better as individuals and as a team."