Christian Malcolm, Dwain Chambers, James Ellington and Mark Lewis-Francis
continued Britain's problems in the relay races as Malcolm failed to pass the baton to Chambers within the set changeover area.
Failure to complete the race should not affect the team's chances of competing at the London Olympics.
The mishap comes a day after the women's 4x100m relay team were disqualified, ruling them out of the 2012 Games, when Hayley Jones was adjudged to have stepped out of her lane.
Malcolm told BBC Sport: "It's my fault. It was up to me as the incoming runner to get the baton across so I take full responsibility for that.
"The turn threw me as I was coming in. I lost momentum as I was going through the acceleration zone.
Chambers added: "We are came here to do well for our country but it was unfortunate that it didn't work out for us. We've got to learn from our mistakes."
Britain's Euro medal haul
Robbie Grabarz, high jump
Mo Farah, 5,000m
Rhys Williams, 400m hurdles
Jo Pavey, 10,000m
Lynsey Sharpe, 800m
Conrad Williams, Richard Buck, Robert Tobin & Nigel Levine, 4x400m relay
Danny Talbot, 200m
In winning her silver, Pavey secured Britain's seventh medal of the championships and her first major international medal. The Exeter Harriers athlete, who was overlooked for a place on the marathon team, added: "It has been nice to have to run the track. I'm really enjoying it, it's making me feel young again."
(32:46.32) finished sixth and ninth respectively.
The women's 4x400m relay squad were just pushed out of the medals as they finished fourth.
Shana Cox, Nicola Sanders, Lee McConnell and Eilidh Child
finished in 3:26.20 as Ukraine took the European title (3:25.07).
In the women's hammer final, British record holder
could only manage an 11th-placed finish with a best effort of 67.17m.
finished fourth in his semi-final of the 110m hurdles (13.55) and
crossed the line in sixth (13.68s), meaning both failed to make the final.
The British Olympic athletics squad is expected to be announced on Tuesday.
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