Eight seeded Indo-Romanian pair made a strong comeback after losing the first set but eventually lost 4-6 6-1 5-10 to the fifth seeds.
They trailed 0-3 in the Super Tie breaker and that cushion stayed with the Italians, who closed the match comfortably in their favour to record their third win a row.
Fognini and Bolleli finished as Group toppers.
Ironically, Bopanna and Mergea won 56 points, six more than their rivals yet ended up on the losing side.