The Belgian-born playmaker struck twice against Sunderland on Saturday to propel himself into the spotlight.
However, the 18-year-old's international future remains in doubt after he turned down advances from the Belgian Football Association to represent their youth squads.
Januzaj, who moved to United in 2011, is also eligible to play for Albania, Serbia and Turkey but England boss Roy Hodgson has confirmed he would be interested in selecting the player once he passes FIFA's five-year residency requirements.
But that would require a change of tact from the FA. The Home Nations struck a voluntary agreement in 1993 not to select "naturalised" players but the Scottish Football Association did lobby for a change in the rules to allow players with five years worth of schooling in the relevant nation to be selected.
Stark, however, is worried that Januzaj's case is a step too far.
Asked about England's hopes of capping the United youngster, he said: "The agreement that the Home Nations have is that we don't use the residency rule and, instead, we have introduced the five-year schooling requirement.
"That's how we got Jordan Rhodes and we just follow those rules.
"For me, international football could be in danger of becoming a laughing stock. You live in a country for two years so end up playing for that country. This might just be me coming from an older generation, but to me that's just not right.
"The five-year schooling rule is valid because the players are brought up in that country and can feel a sense of identity with that country. We probably make it difficult for ourselves because a lot of nations like Germany use the residency rules. Just look at the names on their squad list, they have got a lot of players with Turkish heritage.
"Maybe we are being a bit dogmatic sticking to our agreement but until that changes we should continue with that."
Stark's young squad return to action on Thursday against Slovakia in a European Championship qualifier hoping to make amends for two heavy defeats to England and Holland.
The Dark Blues shipped six goals to the Auld Enemy in a Sheffield friendly in mid-August before surrendering 4-0 to the Dutch last month.
But the manager is convinced those results are not proof of a decline in standards and insists they can bounce bounce back and boost their Euro 2015 hopes.
"The two defeats happened under different circumstances," he said. "For the England game, they had 11 better players who were extremely motivated because they had the England manager in charge that night. They were trying like a beast.
"This sounds like excuses but I've been asked the question so I'm trying to put it in perspective. But we were well skelped and we can't have any excuses.
"It was a one-off game, a friendly against England, and we didn't perform.
"But we said to the players that they have to be big enough to come back from that. And they did. Against Holland, we should have been a couple of goals up by half-time in their back yard. We suffered in the second half but that's the way it happens in international football if you don't take your chances.
"I don't mind people calling me daft for saying this, but on another night we could have come away with a victory. That tells me we can handle it.
"Unfortunately we lost goals in a short space of time in both games. Against England it was four in 20 minutes. That's a wee concern. It shouldn't happen but we hope to address that against Slovakia."