The Light Blues made it three league wins in a row for the first time this season thanks to goals either side of the break from Lee McCulloch and Lee Wallace.
Gers were expected to come out on top of course but they did so minus several first-team stars and McCoist had to make big changes to his starting line-up.
Amongst them was McCulloch’s move from attack to central defence and Robbie Crawford’s first senior start on the right side of midfield.
McCoist said: “Outwith a scare in the first couple of minutes, I thought we were fairly solid and with the greatest of respect, I would have settled for everything we’ve got today.
“We gave an efficient, solid performance, scored a couple of well-worked goals and got a wee break or two as well.
“With the way things have been going, including our two centre-halves hobbling off the pitch at training yesterday, I have to say I’m absolutely delighted with our day’s work.
“Jim (McInally) set up his team in a way where it was solid, really solid, and I think Peterhead are one of the better sides we have played this season.
“He saw us against Alloa, where we were in good goalscoring form, and set up his team in a way to avoid that.
“The one thing about his team with regards to our league is he has one or two players who have a bit of experience of playing at a higher level.
“I think that’s a big benefit for sides when they come to places like this and that showed, particularly in the first half. I thought they were really solid.”
Once more, Rangers’ young players made a contribution and amongst other things, the team began with three teenagers playing in midfield.
McCoist added: “It really is great the supporters are getting to see some of the youths coming through from Murray Park.
“But it’s only good if we continue to win and get promoted. That’s the target and that is what we have to do.
“I did say beforehand that one of the positives to come from our negative situation is we’d get to see some of the younger lads who have come from the academy.
“Even guys like Kal Naismith, who I thought did very well when he came on today during the short time he was on, are gaining experience. That’s a big, big plus for us.
“We’ve got an unbelievably young team and they’re playing again guys, especially this afternoon, who have a bit of experience at a higher level but they’re doing well.”