The Light Blues dropped down to the Third Division this time last year after the newco club were denied entry to the Scottish Premier League following liquidation.
The game north of the border has now had a revamp, with the two league bodies merging to create the Scottish Professional Football League.
The new SPFL brand was launched at Hampden on Wednesday - still without a sponsor - and former Ibrox boss Souness believes the dramatic fall of Rangers is still having an impact on the game as whole.
Speaking at the event at Hampden, he said: "Rangers, by anyone's standards, are a big, big football club.
"I've got a totally biased opinion about them but it would be a fool who thought that the game hadn't suffered by Rangers being demoted.
"The interest, the cash they generate, the interest there would be from sponsors with them being around - I think the game has suffered and I think you would be a fool to deny that."
He added: "They find themselves where they are and they have to deal with that and they will deal with that.
"Ally [McCoist] did a great job last year and will do a great job again this year.
"They have to take their medicine and get on with it and deal with it.
"They find themselves in this league and you can only beat the teams that you're playing each week.
"They did that last year and I expect them to do it again this year."
This season will see Rangers compete in what will now be known as Scottish League 1 - very different circumstances to when Souness was manager between 1986 and 1991.
He said: "It's worlds apart. It's a very different football club. No-one could have imagined this happening.
"But it would appear that the right people are involved now and I have high hopes that in a very short period of time they will be back in the big league and doing well in the big league.
"Walter (Smith) is back involved now and I'd like to think he has a big influence on what's going to happen there."
Former boss Smith was appointed chairman in May, having agreed to return to Rangers as a non-executive director last November.
And, as far as Souness is concerned, the importance of Smith's role cannot be over-emphasised following a period of turmoil at boardroom level.
"It's paramount because he is there for the right reasons," he said.
"He's not there for any other reason than to get Rangers back and make Rangers strong and make Rangers the club that all the supporters have known for over 100 years.
"They are one of the big football clubs in the world, as Celtic are. They are a brand that's up there."