Bookmakers have cut the Ibrox club’s odds to as short as 11/10 in the aftermath of their 2-1 win at Celtic Park on Sunday.
It saw Rangers move just two points behind the reigning champions at the top of the table and with a game in hand as the Scottish top flight clubs begin their three-week winter break.
Gerrard’s men were unable to build on a similar situation 12 months ago when they beat Celtic 1-0 at Ibrox in the final pre-break fixture to draw level on points at the Premiership summit, albeit having played a game more than their Old Firm rivals on that occasion.
Rangers dropped nine points in their first nine league games after the break last season which mirrored the ultimately comfortable winning margin for Celtic as they clinched an eighth consecutive title triumph.
Gerrard is aware that expectations among the Rangers support that this can be the campaign when their club becomes Scottish champions for the first time since 2011 are now at fever pitch. But he is keen to stress that his squad still have much to prove when they return to action next month.
“Listen, the fans are going to be the fans,” said the Rangers manager. “I can only say that in no way, shape or form do we in our dressing room think that we have achieved anything on Sunday, besides a big three points and a big win.
“We deserve credit for that and we will enjoy that, but that is all it is. We respect the challenge. Celtic are still the team because of what they have achieved and the group of players they have got and the form they were in.
“In the dressing room, we won’t get carried away. If other people do, unfortunately I can’t control that except by saying what I am saying to you guys.
“The plan is to try and make it go the distance in the league. That is the plan. But there is a lot of football to be played and a lot of challenges, big challenges, home and away. There are also two other competitions, the Scottish Cup and Europa League, in amongst that and that is for me to try and navigate through with the players and try and do the best we can. But the plan is to try and put in the best fight we can until the end.”
Gerrard, meanwhile, has defended the conduct of his first team coach Michael Beale who was sent to the stand by referee Kevin Clancy during a frenzied conclusion on Sunday which saw Rangers striker Alfredo Morelos sent off for a second bookable offence.
The Rangers coaching staff believed Celtic defender Christopher Jullien should have been shown a straight red card for a challenge on Morelos earlier in the match.
“You have got to respect the position that we are in as well,” said Gerrard. “It is an emotional game and the referee ends up playing more than the four minutes of stoppage time that were initially indicated.
“We get a red card against us and there is one that was blatant against a Celtic player which was not given.
“So understand being in our shoes, it is an emotional time. I am not going to make any apologies. This is new to some of us, so we are not going to get everything perfect, not going to get everything right. My staff and my players have been fantastic and that is all I want to say on it.”