The 34-year-old was the recipient of a barrage of abuse in the hours after his William Hill Scottish Cup horror show against Dundee United at Ibrox as the Gers crashed out of the competition in a 3-1 defeat.
Simonsen gifted striker Nadir Ciftci the decisive goal in the semi-final clash and shut his Twitter account on Sunday.
The Ibrox No.2 will retain his place between the sticks for the SPFL League One clash with Forfar at Ibrox tonight as first choice Cammy Bell continues to be monitored by medical staff after being knocked out in a training incident last week.
McCoist said: "I'm not a Twitter man myself but I was informed last night that there was a lot of abuse and all that stuff.
"Simmo has come in this morning and it seems he closed his Twitter account. (a) It's understandable and (b) It's questionable why he should have had one in the first place.
"That's the way I look at Twitter, Facebook and things like that.
"I just think that, with social networking sites at the moment, you leave yourself open to all sorts of abuse from individuals perhaps who wouldn't normally give the time of day to.
"I've said before that they are responsible adults and they have to be responsible in what they say and do on any social networking site. I know that more than anyone in recent weeks.
"It's not my cup of tea but then a lot of them would say I'm an old dinosaur when it comes to things like that.
"There has to be an upside to it because that many people use it.
"But if someone could enlighten me about it that would be great.
"I don't think it's an age thing with me. I don't think I'd be on it if I was 19 or 20. Maybe I would but I find it difficult to see."