Former Gers midfielder Van Bronckhorst was appointed in succession to Steven Gerrard following the Englishman's move to Premier League club Aston Villa.
Reigning champions Rangers are four points clear at the top of the Scottish Premiership but Van Bronckhorst witnessed their 3-1 defeat by Hibernian in a Scottish League Cup semi-final at Hampden Park on Sunday.
The 46-year-old Dutchman played no part in that match, however, with his work permit not finalised until Monday morning.
Following the loss to Hibs, Rangers defender Connor Goldson said he felt the side had lost a bit of hunger since winning the Premiership.
Van Bronckhorst, however, made it clear at his official unveiling as manager at Ibrox on Monday that he would not tolerate a decline in standards.
"I expect that everyone is on board with me," he said. "It's my duty to prepare players for games. I will prepare them in their attitude, their hunger, whatever.
"For me as a coach and a player, I think the hunger has to come from within yourself. It starts with that. That would make it a lot easier as a coach.
"Being involved in football all my life, I know what needs to be done and what you have to do to be successful. That message I got across as a coach from when I started. I will keep doing that.
"If something or some player thinks otherwise, they will have a tough manager."
He added: "Of course we are not happy with the result yesterday. We can see some things I want to change and we have to be better at.
"But my first meeting with the players will be tomorrow (Tuesday). It's better to tell them first and look them in their eyes, to make sure that from tomorrow on we do everything to be successful with this club.
"That's my goal, that's my ambition. That's the message I want to get through to the players."
Van Bronckhorst's first match as Rangers manager will be on Thursday, when Rangers face Sparta Prague in the Europa League at Ibrox and he admitted taking charge when the season was already well underway had its problems.
"We don't have a pre-season, where you have maybe six weeks or more to work with the players," he said. "For the players also it is something they don't want to have in the middle of the season but it's just the way it is. From Tuesday on we will be working hard to win games."
Van Bronckhorst added he had spoken to Gerrard since his appointment.
"He sent me a message by email which was really nice," Van Bronckhorst said. "I think we will definitely be in contact in the coming weeks to talk about stuff. He did a really great job at Rangers.
"I personally wish him all the best and I'm sure there will be some contact in the next few weeks."
Standout matches today