Gerrard's first match in charge of the Glasgow outfit saw three of his seven summer signings score in a 6-0 rout of League Two side Bury on Friday night.
Ahead of the team's Europa League first-round qualifier on Thursday against Macedonian side FC Shkupi, former Liverpool skipper Gerrard told reporters that his charges must "be ready" to compete for a place in his squad.
"The players have to be ready for the pressure and responsibility of being a Rangers player," the manager said. "If you can't handle it, then you're at the wrong place. It's difficult for me to ask for patience [with supporters]. These fans, they deserve better and want better."
Speaking about the first of four potential Europa League qualifying rounds, Gerrard added: "It's going to be tough to [win all four], but that's what we're here for. We have to deal with Thursday first, though. If you don't approach it with the right attitude you'll face major problems.
"We can't disrespect any opposition. The players will have all the information about them, there can be no excuses."
Rangers meet Aberdeen in their opening Scottish Premiership match on August 5.