The 19-year-old left-back only turned professional in the summer after signing from Queen's Park and has caught the eye with a series of impressive performances for the Tannadice side.
Stark confirmed that Celtic striker Tony Watt, on loan at Belgium side Lierse, was left out due to concerns about his fitness, an issue which has been well-documented in the past few weeks, while 18-year-old Chelsea forward Islam Feruz will join the Scotland under-19s squad which will go to Belarus for the European Championships.
However, on the inclusion of Robertson, a player described by United boss Jackie McNamara as a "revelation", Stark said: "I saw Andy with Queen's Park a few times last season and I was really impressed with him.
"Obviously you are making a judgement of a player playing in the Third Division against players that are playing higher up. But since he has gone to Dundee United he has hit the ground running and he has grasped the left-back position from the off.
"In the first televised game against Partick Thistle he was impressive.
"We have been keeping an eye on him since then and he has been rewarded by getting in and it has been well-deserved."
Turning to the absence of Watt, 19, who was criticised for his fitness and workrate by Lierse boss Stanley Menzo, Stark said: "It has been highlighted over the last week by the Belgium manager.
"He does need to work on his fitness.
"Every time he has come to us he has flagged up that his fitness is not what it should be and it is very difficult for us to gain that fitness.
"I just felt that in the last couple of games, maybe that has shown up a wee bit so we go with ones that are in a good, fit state.
"I will speak to him. I think it will bother him. One thing is, he has always shown up and shown a keenness to be involved."
Scotland host joint group leaders Slovakia at St Mirren Park on 10th October, before travelling to Tbilisi to face Georgia four days later.
The Scots opened the campaign with a 3-0 win over Luxembourg at St Mirren Park before losing 4-0 away to Holland.
Stark said: "They are difficult games. They are both good sides.
"Slovakia qualified for the play-offs in the last campaign and they have three or four players that played in that group.
"Georgia are a good side as well, they are as good as you will get from pot four.
"So we have tough games and we will need to play to our best to get results."