Gers skipper Lee McCulloch revealed at the weekend there had been "four or five different arguments" in the home dressing room at half-time in the Queen's Park match.
The captain's comments have led to speculation that, despite going to the top of the Irn-Bru Third Division for the first time, all is not well in Ally McCoist's pool of players.
Goalkeeper Alexander, though, feels the behind-the-scenes bust-ups underline just how much the Light Blues players want to succeed this season.
And he reckons they show the foreign imports at the Govan club – new boys Anestis Argyriou, Emilson Cribari and Sebastian Faure – now appreciate what it means to be a Rangers player.
"There have been no actual fights," he stressed. "The boys are just hugely disappointed when things don't go according to plan and it shows.
"We all know it has not been good enough at times this term, especially away, for a club the size of Rangers."
Alexander added: "The gaffer has tried to instil in the new boys who have come in what it means to be a Rangers player.
"Having not grown up as fans themselves, they maybe don't know what is expected when you put that blue jersey on week in, week out. A draw is unacceptable. But I think that, slowly but surely, they are learning. They speak to the older players, they hear what the manager has to say and see how the fans react.
"It does take time to understand. Sometimes when you are at another club a draw away from home is acceptable.
"You can also get away with the odd defeat away from home. Not here at Rangers however. They have to take that mental attitude on board. It can be tough to come here and take on all that pressure.
"There is pressure at home because we aren't winning away from home and there is obviously pressure away from home. It builds up. The players who have come in aren't used to that at all.
"But they have to deal with it. The sooner they do the sooner we will become a stronger and better team."
Alexander is optimistic that Andy Little's comeback, coupled with the imminent return to action of David Templeton, will have a huge impact on Rangers' performance levels and results.
Little, who had netted eight goals before picking up a foot injury on International duty with Northern Ireland at the start of last month, came on in the second half of the 2-0 win over Queen's Park.
And manager McCoist is also hopeful that Templeton, sidelined since suffering ankle ligament damage on the artificial pitch at Annan last month, will be ready to return to the fray very soon.
Alexander feels both men have been badly missed by Rangers in recent weeks – and believes their vast experience of Scottish football will prove invaluable.
HE said: "Andy and David being out has been a massive blow. They are two players who will score goals and entertain the fans. We have been missing them. I think that has been obvious in the time they have been out of action.
"They are key players for us. Getting Andy back is like signing a new player. Hopefully, he can get back on the road, scoring goals and helping us out again as soon as possible.
"Andy doesn't need to be told what is required at Rangers. He has been at the club for a long time and knows that.
"The foreigners, though, need to know what the expectations are when they put that blue shirt on and cross the white line before a game."
Rangers return to league duty on Sunday when they play Clyde at Broadwood and Alexander is hopeful they will be able to record their first league win on the road.
McCoist's men have slumped to draws against Peterhead, Berwick Rangers and Annan in the league in the 2012/13 campaign – and lost to bottom-placed Stirling Albion at Forthbank in their last away outing earlier this month.
Alexander courted controversy last week when he claimed referees were failing to protect Rangers stars from foul play in the fourth tier, and is banking on his team-mates being better equipped to cope with the no-nonsense brand of football played in the lower leagues.
He added: "There are a lot more physical players. It is a lot harder. The players get in your faces, put in crunching tackles and don't give you time on the ball. It is difficult to get used to. But, as the weeks have gone on, we are getting more used to it."