Warburton gets his first taste of competitive action at Ibrox on Sunday when Ladbrokes League One side Peterhead visit in the first round of the Scottish League Cup.
Rangers head into Sunday’s game on a high after thrashing Hibernian 6-2 in the second round of the Petrofac Training Cup last Saturday.
Club chairman Dave King has made no secret of his desire to see Rangers win the Championship this season and Warburton said both he and his players are comfortable with that weight of expectation.
“You have to enjoy it,” Warburton said. “You can’t drown under it.
“This is Rangers Football Club and there is that weight of expectation and it is how you deal with it that will determine how well you do.
“Right now the supporters are happy, we had a good result last week, but now the focus is going to work on Sunday.
“That’s what they are, they are footballers, they have to go to work, do a good job and send the supporters home happy.”
Warburton has utilised the experience of former players in assistant manager David Weir and goalkeeping coach Jim Stewart as he prepares his players for the demands of an Ibrox crowd.
The former Brentford manager is setting high standards for his players but the experience of Weir and Stewart has been a big asset as six players line up for their home debuts.
“This is where the knowledge and the experience of the likes of David Weir and Jim Stewart come into play,” he added.
“They have always said to the players that every game for Rangers is a cup final. It has to be that way. Sometimes that term is used too frequently, but it is.
“On Sunday we know we will face a strong challenge from a very determined opponent.
“Playing at Ibrox I’m sure will stimulate any player and we have to recognise that and nullify it and try and dominate the game. If we do that we’ll be okay, and if we let our standards slip then we’ll have a problem.”