The Ibrox side extended their lead at the top of the Scottish League One, with Shiels netting a brace in just his third start this season.
The Northern Irish attacker came in from the cold after suggestions that he would be one of the players heading out of Ibrox in January.
Despite missing out for most of the season, McCoist is optimistic the 28-year-old can prove his worth, with injuries to several starting players.
He said: "We're absolutely delighted with the reaction of Dean. He was obviously a bit concerned about not starting as many games as he'd hope.
"That, obviously, is a good thing for me, because you want that from players who aren't involved.
"He was very receptive to the fact that the team had been winning and it's difficult to dislodge players when you're on a successful run.
"He quietly waited for his chance and with the injuries we saw today, he came in and he played particularly well.
"He was drifting into wee pockets behind their midfield and in-front of the back-four and his two finishes were excellent.
"I really hope he can kick on from here. He only came off because he looked quite tired. He's a determined boy who should do well and he's made it clear to me he wants to be in the team."
With the focus on the club's finances in recent weeks, McCoist has had several discussions with chief executive Graham Wallace over where the axe will fall with regard to their excessive costs.
Addressing supporters in the Rangers matchday programme, Wallace refuted suggestions that the intended cost-cutting across the board would impact the ambitions of the club on the pitch.
He said: "Contrary to what you might read in the press, this is not solely about cutting costs but is about identifying what we need in all areas of the club in order for us to be successful.
"This will also mean additional spend in certain areas will be required.
"Much comment has been made externally about changes to the playing squad potentially impacting the quality of the team.
"However, let me be very clear that our focus is to build teams that are capable of challenging for on-field success in every competition and we have a focus that looks at both short and longer term needs.
"The first team is naturally the major area of focus but our philosophy extends throughout teams at all age groups.
"Alistair and I are working on our player strategy but we are not just focusing on what we need today, but what we will need for next season and the seasons beyond that."
East Fife boss Gary Naysmith remains optimistic the Methill outfit are on the right-tracks after an encouraging display at Ibrox.
He added: "We got off to a really disappointing start. The first three passes from the back straight to Rangers players gave them the initiative.
"We gradually grew into the game. But definitely in the second-half at 1-0, we had some good chances. It would have been interesting game if we had gone level.
"I couldn't ask any more from the players. It was important we showed we were improving as a team."
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