A nail-biting 2-1 win over South Korea on Saturday means the Scots will face rivals England on Wednesday for a place in the final.
Chelsea youngster Billy Gilmour and West Brom winger Oliver Burke scored early goals, as Scotland held on to their unbeaten record.
Gemmill, who played in the Premier League for Nottingham Forest and Everton, described his pride for his team.
He said: "It’s satisfying to go through the group unbeaten and get more points than last year.
"I would have liked clean sheets but that’s setting the bar very high.
"A lot of people in Scotland question where the young players are.
"Performances like this help convince people good work is happening. Not just with us but, more importantly, with the clubs.
"We have got a lot of players who weren’t able to come because of injuries but we take confidence that we’re starting to put together a real squad of players, even outside of this group. We have a bigger selection and real depth.
"We’re really proud of the players and it’s great justification for [performance director] Malky Mackay, who found the budget to get us here because it costs a lot of money."
Speaking on the prospect of facing England, he added: "Every time the teams meet there’s a real sense of occasion. It’s going to be the same again this time.
"We are going to need every ounce of energy to find a way to win."
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