First half goals from Ian Black, Lewis Macleod and Lee McCulloch secured an easy win but McCoist, who scored a hat-trick in a 5-0 victory the last time the sides met in 1992, is keen for them to take full advantage when they are dominating a game.
"If I was playing today, I would have looked on that as an opportunity to batter a few goals in to get the goal tally up," he said.
"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."
But McCoist was pleased to claim a win on the road at the first attempt after they recorded three draws and a defeat in Scotland's bottom division last season before eventually securing their first away win in the league last October.
"It's been well documented that we didn't start well away from home last year," he added.
"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 (a shock defeat in the Scottish League Cup) was a one-off. To come down here and win comfortably 3-0 was pleasing."
McCoist also confirmed he has extended the trial period of former Everton goalkeeper Steve Simonsen after he trained with the club this week.
"He's coming back up on Monday morning for another week and we will see where that takes us," he said.
"He has shown up really well and we will get a chat with him when he's back up."
Meanwhile, Stranraer boss Stephen Aitken was left frustrated after his brother Chris was sent off 18 minutes from time for a second bookable offence.
"I was disappointed with him," he said. "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.
"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."