Kyle Lafferty scored the only goal in the second half for the champions, after Steven Whittaker missed from the penalty spot just before half-time.
The win also allowed Rangers to stretch their advantage over Celtic to 10 points ahead of their rivals' own game against Hearts on Sunday and McCoist says he would have loved the opportunity to keep the momentum going.
He said: "It's a disappointment. I wish we were playing next week, there is no doubt about that.
"But I'm just the same as everybody else now, I'll just look out the tartan scarf and bunnet and be cheering the [Scotland] boys on.
"In terms of our momentum, it has been good. We wish all our players all the best and the most important thing from our point of view is that they come back safe and sound. It's a concerning time for managers and coaches."
Rangers now boast a healthy lead at the top of the SPL, with Stuart McCall's Motherwell sitting in second spot thanks to their win at Dundee United.
McCoist added: "It was a brilliant result for wee Stuart today at United that puts them into second place and obviously Celtic are at Tynecastle on Sunday.
"Everybody is talking about gaps but we just wanted to win the game. The three points were far more important than any gap.
"It's been a good week for us and we got another clean sheet so that was really pleasing."
Whittaker had to battle team-mate Nikica Jelavic for the ball when the penalty was awarded, only to balloon well over the crossbar, but McCoist would have no problem with the full-back stepping up again.
He said: "I think Jelavic did want it. I would be very surprised if he didn't and I was very surprised that he didn't get his way.
"But, to be fair to Steven, Steven is pretty strong-willed and he fancies himself in that position. You don't score them all. I would have no problems with Steven taking the next one.
"My problem would be if nobody wanted to take the next one. If they are fighting over it again, I don't mind.
"I'm not sure we have a designated penalty-taker and I don't think you should have a designated penalty-taker.
"I'm firmly of the belief that whoever fancies it should take it.
"In my opinion, if somebody is not playing well and they are the designated penalty-taker, the pressure is right on them to say 'No, I don't fancy it'.
"It's the right thing to do but it's the hardest thing to do."
Hibs boss Colin Calderwood felt there were encouraging aspects of their performance but had no real complaints about the result.
He said: "On reflection, they had better chances in the first half and we had a good chance in the second half.
"But we would be kidding ourselves if we thought overall that deserved us the win.
"I quite liked our performance and I think we grew into the game. We didn't have the danger that we had in the first half, so that's encouraging.
"But, in the end, it was the quality and the same type of ball that undid us and won the game for Rangers."
Ivan Sproule appeared to be unhappy when he was withdrawn in the second half and Calderwood was asked if there was an issue with the player.
He said: "Apparently so, but nothing that will worry us."