The 35-year-old closed his Twitter account after the abuse received in the wake of his error, which gifted Tannadice striker Nadir Ciftci the clinching third goal at Ibrox on Saturday.
Simonsen was drafted in for only his second game since joining the Scottish League One champions last season after Cammy Bell suffered concussion, and may remain in goal for the clash with Forfar at Ibrox on Tuesday night if the Gers number one is not declared fit.
However, McCoist all but dismissed the former Everton, Stoke and Dundee keeper's Twitter decision.
"It makes me feel he shouldn't have been on it in the first place to be quite honest," he said.
"Maybe I am an old dinosaur but I am seeing more negatives than positives from players on Twitter at the moment.
"I have said before, we have to be extremely guarded in what we do and what we say.
"Of course it was a mistake, an error, he is the first one to admit that.
"He also had probably the best save I've seen this season up at Forfar, one of the best three I've seen anywhere this season, so you take the good with the bad.
"As I say, on these social network sites you run the risk of taking abuse from a certain type of individual."
McCoist retained his arms-length policy about the club's seemingly-endless boardroom squabbles, but insists they do not alter his belief that Rangers will get back to where they were before administration and liquidation in 2012 resulted in them relaunching in the bottom tier of Scottish football.
The row between Dave King and the Rangers board intensified on Sunday night after he issued another statement questioning its integrity.
The former Ibrox director on Friday urged Light Blues fans not to buy season tickets and accused the board of an ''extreme act of bad faith''. The South Africa-based Glaswegian was upset that the club have asked fans to renew their season tickets before the completion of a 120-day review of the business's operations.
Rangers, who have referred the matter to legal advisers, noted King's initial statement ''with astonishment'' and said he had made ''a number of untrue allegations'', but have not responded to his latest comments.
McCoist said: "If you don't believe and don't have faith in the club moving forward then you are in the wrong job, and I have to be confident in that.
"I just look at the atmosphere our supporters created on Saturday and that tells me we have a chance.
"Our job is to go on to the park and win games of football and thankfully, more often than not, we have been doing that.
"And as I say, when you look at the atmosphere that we created inside the stadium on Saturday, that's why we need to keep believing.
"It is a hard enough job to do and if you let outside factors affect you then it is exceedingly difficult.
"So we have to batten down the hatches and concentrate on the football, which we did on Saturday."
Meanwhile, the Ibrox club announced a new three-year shirt sponsorship deal with online casino company, 32Red, which starts from July.
Rangers chief executive Graham Wallace said: "We are in the process of rebuilding Rangers Football Club, and alliances with blue chip companies such as 32Red will assist us on our journey back to the top of Scottish football.
"We would like to thank our current shirt sponsor Blackthorn and Tennent Caledonian Breweries for their ongoing support of the club during a very difficult period."