Even so, Britain's men achieved their fifth European Cup success, boosted by further individual victories from Marlon Devonish and Andy Baddeley.
Devonish fought a tough battle in the home straight with Anastasios Gousis before steering clear of his Greek rival over the final strides of their 200m encounter.
"I did my job," said Devonish. "But my race was not very good technically. I had some difficulties to keep my speed until the end. I'll have to work on that."
Baddeley, a revelation when breaking 3min 50sec to win the Dream Mile in Oslo a fortnight ago, showed again what an improved middle-distance runner he is.
Stepping up to 3000m, he zig-zagged up the track past Spain's European 5,000m champion Jesus Espana, who had nothing left as Baddeley edged ahead to win in 8min 01.28sec.
The women, after struggling in the early stages of day two through lack of top-class field event performers, turned up the heat on the track to take third place behind Russia, winners for a 12th successive time, and Ukraine.
No one matched the 400m and 800m victories of Nicola Sanders and Jenny Meadows on the opening day but Christine Ohuruogu, Kate Reed and Jade Johnson with their second places, provided a solid platform for the podium finish.
Ohuruogu, the world 400m champion, powered down the straight to cross the line behind France's defending champion Muriel Hurtis-Houairi in 23.23sec.
Reed, defying the intense heat, recovered brilliantly after falling off the pace with five laps to run to clock 15min 40.73sec and finish second behind Ukraine's Nataliya Berkut.
Johnson, who has failed to consistently reproduce the form which won her Commonwealth and European long jump medals in 2002, again emerged as a world-class performer when leaping a lifetime best of 6.81m as Russia's Lyudmila Kolchanova posted a world leader of 7.04m.
