The Linnets made a sorry departure from their Setanta Shield debut on Tuesday night.
Keith Webb's side were out-classed by a weakened Tamworth outfit, who cruised to a 2-0 lead inside the firs 25 minutes and ran Lynn ragged for the first 70 minutes of the match.
A late goal from Julian Joachim woke Lynn up and set up a gripping finale, but a young and competent Tamworth side deservedly booked their place in the next round.
Linnets boss Webb said: "I thought we were very poor, especially in the first half.
"I've gone in at the interval and read the riot act and the players have responded a little bit in the second half.
"But you can't take anything away from Tamworth. They care here, worked us and caused us a lot of problems. we just weren't at the races."
Lynn made three changes from their starting line-up against Fleetwood on Saturday while Gary Mills' Tamworth made six, leaving key strikers Nick Wright, Alex Rodman and Gareth Sheldon on the bench.
Tamworth's teenage strike force of Dean Lea and Cameron Jones (both 19) gave the Linnets' defence a torrid time, while the impressive Bradley Pritchard pulled the strings in the Lambs' midfield,.
The Walks outfit were given an early warning of what was to come when Howie saved well from a Jones' cross in the opening exchanges.
But there was little Howie could do about Tamworth's opening goal in the second minute when Pritchard few the ball through to Jake Sheridan to rifle home an unstoppable shot.
Lynn were sloppy with the ball and lacked ideas all over the pitch, while Tamworth caught the eye with their attacking brand of football.
Their second strike came as no surprise in the 25th minute when Lynn conceded possession and Sheridan knocked a Jones cross into the path of Pritchard to nod home.
The Linnets' best effort of the half came 12 minutes before the break when Danny Bloomfield saw his header superbly turned around the post by Tamworth keeper Will Puddy following a Joe Francis free-kick.
Howie was alert to foil Dean Lea as Tamworth ended the half as they had started it - well on top.
There was a slight improvement from the hosts after the break, but it was The Lambs who missed a great opportunity to make it 3-0 when Lee Hildreth's drive was saved by the body of Howie in the 63rd minute.
The introduction of Andrew Fisk gave Lynn a little bit more bite in midfield and the brief appearances of both Michael Frew and Julian Joachim added more pace to Lynn's forward play.
Twice Lynn were wasteful from free kicks in good positions, but they gave themselves a lifeline in the 78th minute when Frew's centre was knocked back by Ben Sedgemore into the path of Joachim to smash the ball into an empty net.
From this point there was only one team in it as Tamworth began to lose their shape and legs and Lynn sensed an equaliser in an exciting finish.
Tamworth, superbly marshalled by Craig McAughtrie at the back, were forced to defend for the lives as Lynn peppered their box with crosses.
But Lynn's brief fightback was all too late as Tamworth held on to progress through to the next stage.
|Lynn: Howie, C Defty, Smith, Peters, Weaver, Sedgemore, Turner (Fisk 56), Mitchell, J Defty, Bloomfield (Joachim 67), Francis (Frew 64). Subs (not used: Kelly, Murray.
Goal: Joachim (78).
Tamworth: Puddy, Burgess, Law, McAughtrie, Wylde, Warburton (Langdon 83), Pritchard, Hildreth (Sheldon 81), Lea, Jones (Smith 81), Sheridan. Subs (not used): Wright, Rodman.
Booking: Smith. Goals: Sheridan (2), Pritchard (25).
Referee: S Feerick (Peterborough). Attendance: 510
Stats (Lynn first): shots on target 6, 6: off target 4, 2: corners 5, 1: offside 1, 5; free kicks 12, 21.