I've heard the opposite: that the large, high-thrust engines needed on twin-engine wide bodies for takeoff and ETOPS certification can have greater aerodynamic and performance losses at cruise, as well as higher maintenance costs, than the smaller engines on four-engine wide bodies. And in the specific case of the A380, having four engines did not put them at a fuel economy disadvantage, notwithstanding the widely held belief that it did.
A greater difference in fuel economy, however, comes from the generation of the engine. The A380 is no longer cost efficient not because it has 4 engines, but because those 4 engines are 1.5 generations behind modern engines.[1] Airbus and Emirates killed the A380 mere months after Rolls Royce firmly shut the door on developing an engine upgrade, and the whole multi-year saga hinged the entire time on Rolls Royce's vacillations. (Of course, Rolls Royce wouldn't invest in the engine because the market was too small, and they were also struggling with other issues that required their time & capital, but those are different matters.)
[1] Likewise, the 747 was less efficient than the 777 partly because the 777 was equipped with a newer generation of engines. But this difference was never factored into the calculus that gave rise to the belief that two engines were inherently more efficient than four, regardless of context.
A greater difference in fuel economy, however, comes from the generation of the engine. The A380 is no longer cost efficient not because it has 4 engines, but because those 4 engines are 1.5 generations behind modern engines.[1] Airbus and Emirates killed the A380 mere months after Rolls Royce firmly shut the door on developing an engine upgrade, and the whole multi-year saga hinged the entire time on Rolls Royce's vacillations. (Of course, Rolls Royce wouldn't invest in the engine because the market was too small, and they were also struggling with other issues that required their time & capital, but those are different matters.)
[1] Likewise, the 747 was less efficient than the 777 partly because the 777 was equipped with a newer generation of engines. But this difference was never factored into the calculus that gave rise to the belief that two engines were inherently more efficient than four, regardless of context.