Ally McCoist believes most Rangers fans would accept steady improvement from their team, rather than demand they clinch this year's Scottish Cup.
The Gers have not won a major trophy since entering administration in 2012 and re-emerging in the bottom tier of Scottish football.
They tackle rivals and holders Celtic in next month's cup semi-final.
"The first trophy since the club has been in trouble is very important," ex-Gers striker and boss McCoist said.
"I don't think it's the be-all and end-all that it happens this year.
"It would be great for the supporters if it happened this year. But as long as there is continued improvement and a better level of quality of player that comes in, I think most fans will be reasonably satisfied with that."
McCoist, 55, managed Rangers between 2011 and 2014, winning the third division (now League Two) and League One titles.
He believes the club's current boss, Graeme Murty, has done "a more than reasonable" job this season after moving up from the under-20s to take over on a caretaker basis in October - when Pedro Caixinha departed - before being given the role until the end of the season two months later.
Murty's long-term future has been subject to much debate after successive home defeats by 10-man Celtic and Kilmarnock this month but McCoist said: "Obviously it was a couple of bad results for Rangers but overall, looking at it fairly, I think Graeme has done a good job.
"Some of the signings that have come in have improved the team and improved the squad and, as I say, he has done a more than reasonable job.
"I felt Celtic deserved to win the game but the last two Old Firm games could have gone Rangers' way.
"That said, Celtic have a better quality of player, certainly in forward areas but I certainly think if there is sensible reinvestment in the Rangers squad that will continue to close the gap."
'Celtic have a hoodoo over Rangers'
Former Celtic striker Simon Donnelly believes Rangers are experiencing the same sense of powerlessness he felt for a time at Parkhead in the 1990s.
When Donnelly made his Celtic debut in 1994, Rangers were domestic treble winners from the previous season before their Old Firm rivals stopped them achieving 10 titles in a row in 1998.
The tables have turned since then with Celtic looking for back-to-back domestic trebles this season and unbeaten against Rangers in nine games ahead of their semi-final showdown at Hampden Park.
Brendan Rodgers' men go into the game bolstered further by a 3-2 Scottish Premiership win at Ibrox earlier in the month after falling behind twice and finishing the game with 10 men.
"Celtic kind of have a hoodoo over Rangers at the moment," Donnelly, 43, said.
"I experienced that myself back in the day but it was the other way around. It is not a nice feeling and it plays on you.
"I think it played on them at Ibrox. There was that lack of belief as Celtic came back twice.
"I remember being in games and doing really well and they would go up the park and score, whether it was Brian Laudrup, Ally McCoist or Paul Gascoigne. It was difficult to turn that wave.
"You could argue that [Alfredo] Morelos should score at the end to get them a draw but the longer the run goes the harder it gets.
"I would expect Celtic to win the semi-final. They are going for a back-to-back treble and I think they have the players that will edge it."