Schick doubled that lead in the 52nd minute with a sensational effort from just over the halfway line which beat keeper David Marshall.
After the pre-tournament hype, it was a dispiriting anti-climax for the Scots, who could not get control of the game albeit they passed up several opportunities.
Steve Clarke’s men will immediately start preparing for the trip to Wembley to play England on Friday night before their final group game against Croatia next week, but already their task looks ominous.
Scotland have never qualified for the knockout stages of a major tournament and will have to find something special to end that poor record.
The Scots’ return to the big stage was a long time coming and the Tartan Army may have had early concerns when it was revealed defender Kieran Tierney would miss out with a knock.
Scotland had beaten the Czech Republic home and away in the Nations League last year and confidence was high, demonstrated by a forceful start.
The game settled, however, and Jaroslav Silhavy’s side began to edge forward with menace.
Marshall made a good save from Schick’s 14-yard drive after midfielder John McGinn lost possession at the edge of his own box.
The Scots responded and Dykes side-footed a cross from skipper Andy Robertson just past the front post.
The Czechs were the more comfortable side but in the 31st minute Christie got on the end of a loose ball and set up the unmarked Robertson on the left, only for his rising drive from 20 yards to be tipped over the bar by keeper Tomas Vaclik, with the corner defended.
Scotland would soon pay for that miss.
Czechs forced three consecutive corners of their own before Schick rose above defenders Grant Hanley and Cooper to head in a cross from Vladimir Coufal.
Adams replaced Christie for the start of the second half but it was the Czechs who drove forward for a second goal, with Marshall making good saves from Schick and Vladimir Darida.
Then, as the Scots kept up the pressure, they found themselves two down from a Czech break when Schick beat the backtracking Marshall with a remarkable shot from just inside Scotland’s half.
The Tartan Army were stunned, the few dozen Czech fans ecstatic.
Scotland rallied once more but Vaclik made two key saves from Dykes which prevented Clarke’s side getting a lifeline, while Armstrong’s deflected shot ended up on the top of the net.
Clarke changed it up again in the 67th minute, bringing on Ryan Fraser and Callum McGregor for Armstrong and Hendry before Kevin Nisbet and James Forrest came on for O’Donnell and Dykes.
The Scots kept plugging away but Marshall had to make a good save from substitute Michael Krmencik to prevent a third and from the pre-match cheers, came the post-match disappointment.