McGhee made a goalline clearance during the stalemate, denying Aaron Doran what could have been the winner on 80 minutes.
Speaking after the match, McGhee said: "They broke on us and Harry (Burgoyne) has gone out to make himself big.
"Once the keeper does that, the first reaction of a defender is to try and get behind him and chuck your body in front of it. Luckily, I have managed to read where he is going and get a leg on it."
It was a dramatic moment that helped secure a point for the Bairns at a difficult venue - and McGhee insists it's a point gained.
"It's a tough place to come Inverness, they are a good side that are doing well in the league and they are up there for a reason.
"It's a good hard-fought point, we could have knicked it at the end when Shayne (Lavery) had a wee half chance but I thought the boys played really well.
"I thought the first half was one of the best we have played since we have been together. It's encouraging."
The big down side on the day was results elsewhere - with the rest of the bottom four winning - but McGhee says the Bairns are positioned well to stay up.
"You see the results coming in, but it's in our hands and we are in a good position.
"From where we were at the start of the season and at Christmas time till now - we have come on leaps and bounds. We just need to go out every game and get three points."
Tomorrow's opposition, Queen of the South, were one of the teams in the bottom four that won - beating Dundee United 2-1 at Tannadice to end a run of seven straight defeats.
"It's obviously a good result for them," McGhee added. "But again this is a good result for us and this is a tough place to come and we played well.
"We are more than capable of going down there and getting a result and that's what everyone in the dressing and at the club will be striving for."