Nicky Clark scored four goals, while Lee Wallace and skipper Lee McCulloch were also on the scoresheet to leave McCoist delighted.
"It's a fantastic achievement for the players. They can be very proud of that run at the moment but it has to continue on Saturday against Ayr United," he said.
"People will look at the opposition and say this, that and the next thing.
"But, as we have seen this year in the cup competitions, the teams in the lower leagues are more than capable of winning games against teams with supposedly better squads.
"It's a great achievement and the boys will get the credit they deserve from ourselves and that's all that matters really."
Despite a stunning start to the campaign that has seen them win all 14 league matches to date, McCoist is not convinced they will win every league game this season.
"I genuinely don't think so. I really don't think that will happen," he added.
"Anybody who has been to our away games at Forfar and Brechin this year will know how difficult it is and that's why I just don't think it will happen.
"I will settle for winning the league, that's what I will settle for."
But Forfar boss Dick Campbell disagreed with McCoist.
"Part-time clubs will struggle against them because they've got better players and they will win games," he said.
"They are top of the league and they'll have it won by Christmas. They can put a reserve team out in the second half of the season and no one will be near them."
McCoist also reserved some special praise for Clark, who scored 40 goals for Queen of the South in the same division last season but has taken his time to get going for the Light Blues.
"Nicky has battered a few goals in, which will be great for him, against a team who have provided us with difficult games so far this season," said McCoist.
"I think a lot of people, wrongly in my opinion, automatically thought he would just come in (and score goals) because he scored 40 goals last year with Queen of the South.
"He continues to work hard and, when you do that, you've always got a chance of getting your rewards. This was a great day for him."