They lost a penalty shoot-out 5-3, with Jack Concannon having his spot-kick saved.
Blues had gone into a ninth minute lead against the Southern Premier Central pacesetters, Ryan Stirk following up after Concannon burst through and had a shot parried.
And they looked in control of the First Round tie.
But Tamworth got a foothold back in the game and equalised in the 51st minute when Dan Creaney played Rhys Hoenes in down the right and he struck a fierce attempt high past Moha Ramos.
The contest might then have gone either way but it went to penalties and Tamworth dispatched all of theirs.
Ramos was unable to keep one out although Tamworth's second kick, from Bilal Yafai, crashed off the underside of the crossbar and the referee judged it to have crossed the line.
For Blues, Stirk netted the first kick, Concannon's blast down the middle was blocked by 'keeper Richard Walton, Joe Redmond scored as did Kyle Hurst. But Blues were always playing catch-up and it was left to Creaney to stick his kick low to the right past Ramos to give the hosts the victory.
Blues started brightly and moved the ball around with confidence, forcing Tamworth to chase shadows.
Concannon broke in down the right channel and let fly, forcing a parrying save and Stirk was there to open his body up and sidefoot the loose ball home.
Two minutes later Blues might have extended the advantage when Oumar Traore cut a ball back from the right and Jayden Reid switched onto his left foot and steered a shot from outside the area that clipped the top of the netting.
After Tamworth began to get to grips with Blues football and challenged them higher up the pitch, the visitors lost their thread somewhat.
But two minutes before the interval there was another chance, after a switft counter, triggered when Stirk broke up play from a dangerous ball into the box.
Concannon swapped passes with Nick Kinina down the right and drove on into the Tamworth box, challengers in his wake, but placed a well struck shot just wide of the far post.
Tamworth came out with plenty of gusto in the second-half and caught Blues out with the leveller, Hoenes finishing smartly.
Ramos then saved a sidefooted lob after a Creaney flick-on sent Hoenes away and after a carbon copy approach by Tamworth, he made a crucial stop, with his feet, as Hoenes got into a better position to score.
Concannon and Hurst went very close to finding the bottom corner with efforts from outside the box as Blues rallied.
And after substitute Josh Williams added impetus, and went round the last defender wide on the right, his cross went just behind Traore on the opposite side of the area.
In the final actions, both Tamworth and Blues might have nicked it.
Creaney turned a left wing cross over the bar from close range and after Williams and Remi Walker combined to prod a ball for Kinina to latch onto, it looked as if he would elude the defence and go one on one, but he was crowded out by last-ditch defending by the red shirts.
Blues: Ramos, Kinina, Roberts, Stirk, Bajrami (Redmond ht), Gordon, Concannon, Campbell, Hurst, Reid (Williams 64), Traore (Walker 78). Subs not used: Rouse, Burke.
Report: Crewe Alexandra Under-23s 0 Blues Under-23s 3
Report: Bristol City Under-23s 2 Blues Under-23s 1