Suduva striker Ivans Lukjanovs' late winner condemned TNS to a tenth successive European defeat.
The 21-year-old's 85th minute strike confirmed a 2-0 aggregate victory for the Lithuanian side in Thursday's UEFA Cup qualifier at Newtown's Latham Park.
TNS wanted to break their European duck and progress past the first qualifying round for the first time.
Saints had two good chances. Tommy Holmes' shot was tipped round the post, and an Alfie Carter effort was blocked.
But like in the first leg in Marijampole, the Welsh Premier runners-up were beaten by a late goal.
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