But the keeper insists the League One champions can't afford to settle for second best.
With Ibrox No.1 Cammy Bell out with a shoulder injury, deputy Simonsen is set to retain his place between the sticks for the visit of Dumbarton this afternoon.
It hasn't exactly been the start to the season boss Ally McCoist would have hoped for from his side, with the Gers losing to Hearts then struggling to see off Falkirk in their opening second-tier fixtures.
The Sons showdown gives Rangers a chance to kick-start their SPFL Championship title challenge.
Simonsen knows ensuring the silverware is in the trophy room come the end of the season is the only way to satisfy an expectant Ibrox crowd.
"I think it's fair enough for the fans to expect us to win the title," he said.
"As players, we know we must go out and win this league. That's the aim from the start. We know what standards are expected here.
"The aim is always to win the league. We showed that last season when we won it very early on. Then we didn't take our foot off the pedal but went on to finish undefeated.
"This season we want to win the Championship, as much as anyone can want it."
Simonsen watched on from the sidelines for most of last season as Bell helped Rangers to the League One title, and he had mixed fortunes in the games he did play for the Light Blues.
A superb showing against Forfar was overshadowed by a costly blunder in the Scottish Cup semi-final defeat to Dundee United at Ibrox.
The fall-out saw Simonsen close his Twitter account after getting online abuse but the 35-year-old keeper insists those unsavoury events have not left a sour taste.
And Simonsen insists he has moved on from the high-profile blooper and its aftermath.
He said: "At the time of the Dundee United game it was very disappointing.
"But as time goes on, you learn to take the rough with the smooth. I'm a pretty strong character, so I can deal with stuff like that.
"If needs be, I will shut my account again and re-open it or whatever. It's not a problem.
"It was maybe a slight eye-opener in terms of the scrutiny that is placed on every single player who walks across the white line here.
"But it is part and parcel of being a footballer at this club. You've got to be able to deal with those situations.
"It certainly was an eye-opener but, like I say, I've moved on from that. Hopefully it won't happen again."
Now Simonsen has a chance to ensure that he will not be remembered for that mistake as he targets a prolonged spell in McCoist's starting line-up.
After leaving Ibrox at the end of last term, he put pen to paper on another deal during pre-season.
And the former Everton and Stoke shot-stopper is pleased to be back on the Light Blues' books after being on the lookout for a club.
"I did have options at first," Simonsen said.
"I was mulling over a few things - some down south and one up here, as well.
"But as soon as I got a call from the manager saying he wanted me back at Ibrox, it was an easy decision.
"There were a couple of things going on and, to be fair to the manager, he kept me in the loop.
"He had wanted to keep me but there were things in the background that needed to be sorted out.
"The gaffer kept in close contact and let me know what was happening. It was a delight to come back.
"I think every footballer wants to be part of a big football club, with good traditions and a fantastic fan base.
"For me, getting on a bit in my career and having dropped down the leagues a bit, I had played for some big clubs.
"But this is a huge club and it was difficult to turn down their offer. It was a no-brainer.
"There was interest from other clubs but it didn't get further than that.
"As soon as Rangers were the option, I turned down everything else."
Bell is set to be sidelined for a couple of weeks more as he recovers from the shoulder injury he sustained at Falkirk last Friday night.
It means Simonsen has a chance to stake his claim for the Ibrox gloves this season.
He conceded a late goal in the rout of Clyde on Monday night but is now determined to impress boss McCoist.
Simmo said: "It was nice to get on the pitch the other night and to be part of a good team performance.
"It would be great to get a few games on the spin under my belt now.
"I was obviously very disappointed to concede a goal.
"For us boys at the back, keeping a clean sheet is just as important as scoring a goal is to the boys up front.
"I think that sometimes you need to look at the bigger picture and realise that we put in a good performance."