They have won five from five, with impressive wins over FC Midtjylland in the Europa League and a 6-1 thrashing of Hibernian in the Scottish Premiership.
One of Rangers’ most impressive feats of the summer has been keeping Alfredo Morelos amid heavy transfer speculation.
The forward scored twice in the rout of Hibernian, before another brace against Midtjylland.
And Mcallister believes maintaining consistency across all three competitions will be key for Rangers this season.
Rangers beat FC Midtjylland in the Europa League (Image: GETTY)
He told The Evening Times that Rangers now have the winning mentality that Gerrard was keen to instill in his players.
“The games against Legia Warsaw are crucial for us, I feel,” McAllister said.
“I think the profile of the club doesn’t half take a hike up if we get to the Europa League proper again.
“I loved the games against Villarreal, Spartak and Rapid at Ibrox last season.
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Gary McAllister is happy with the squad's mentality (Image: GETTY)
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“Big games under the lights at Ibrox, against those top end clubs, are something that just take our players up another level.
“Because you have to be really switched on in those games.
“The fact you are going from that back into a domestic game, which is totally different, takes a different type of mentality.”