Ian Black's strike was deflected home by Andy Little for an early opener, before goals from Lewis Macleod and Lee McCulloch wrapped up the three points at Stair Park.
But McCoist - who netted a hat-trick in a 5-0 win the last time the sides met in 1992 - felt Rangers should have won the match even more comfortably.
He said: "If I was playing, I would have looked on that as an opportunity to batter a few goals in to get the goal tally up.
"I don't just mean the forwards, I mean the midfielders as well.
"We definitely have to be more clinical in our approach to scoring more goals and killing teams off.
"The best way to show the opposition respect is to continue to play in the same manner for the entire 90 minutes no matter what the score is and I didn't think we did that in the second half."
However, McCoist was thrilled to secure victory from their first away fixture in the league after struggling on the road in Scottish football's basement division last term.
The Light Blues endured three draws and a defeat before eventually picking up their first away win in the league in October last year.
He said: "It's been well-documented that we didn't start well away from home last year.
"We struggled to come to terms with the natural aggression and the tempo in the division.
"We were all very hopeful that wouldn't be the case this year and I'm hopeful the Forfar game was a one-off. To come down here and win comfortably 3-0 was pleasing."
There was debate over whether Black or Little should be credited with the opener and, when asked who was claiming it, McCoist said: "Both of them.
"Black said it was going in anyway, which I would have expected him to say.
"I think it's actually the referee's decision but I would have given it to Black so that's me probably off Andy Little's Christmas card list."
Meanwhile, Rangers have extended the trial period of former Everton goalkeeper Steve Simonsen, who trained with the club this week.
McCoist said: "He's coming back up on Monday morning for another week and we will see where that takes us.
"He has shown up really well and we will get a chat with him when he's back up."
A difficult day for Stranraer was made worse when they were reduced to 10 men following the dismissal of Chris Aitken with around 20 minutes to go.
Boss Stephen Aitken - his brother - said: "I was disappointed with him.
"As players on the park, when you're on a booking and the game is going away from us, the last thing you want to do is get sent off.
"It was a stupid sending off to get, especially in a game like that. But these things happen."
He added: "I can't fault the players for effort, I thought they gave a good account of themselves. We can concentrate on the rest of the season now."