Responding to Glamorgan's 282 in the first innings, Derbyshire could only muster 203 in 54.1 overs in the second day's play.
Pujara, who came to bat at No.4 after Derbyshire had lost both their openers early, tried hard to grind it out in his 26-ball stay but was finally trapped LBW off Glamorgan medium-pacer Jim Allenby.
The Saurashtra batsman did hit a boundary in his 27-minute short stay at the crease but mostly looked suspect on a seaming Sophia Gardens wicket.
The Rajkot-born player had accumulated 222 runs at an average of 22.20 in the five Tests with just a single fifty to his credit.
Pujara has replaced West Indian great Shivnarine Chanderpaul in the Derbyshire team as its overseas player.
Meanwhile upcoming Indian pacer Varun Aaron, who signed up with Durham in place of Australian all-rounder John Jastings, is also soon going to join his County side for its remaining fixtures.