Stark admitted to being disappointed by Scotland's second-half display but they were able to make the most of two early Jordan Rhodes goals to secure the spoils in their first match since Craig Levein's dismissal.
The Scotland U21 coach is in the running to take over, but he was not thinking about his future and was happy to focus on getting the national side back on track after Levein's winless final four games in charge.
"We won and that's the most important thing," said Stark.
"When we approached the game we felt we needed to win the game. On the back of that you hope we would have a scintillating performance.
"We would concede it wasn't quite that but the first half we were comfortable and we created some chances We felt at half-time that the game could go two ways, we can begin authoritatively and not give Luxembourg any encouragement and build on the position we were in but unfortunately we lost a goal from a free-kick.
"You have to sometimes credit the opposition, Luxembourg got great encouragement from that and defended resolutely but also used the full pitch and made life difficult for us.
"You wouldn't say we were absolutely sure we wouldn't lose a goal because they had some big players and we had to defend some free-kicks, one or two of which were pretty debatable, especially the one the goal came off.
"We are a wee bit disappointed we weren't able to build on the half-time lead."