Craig Beattie put the Swans ahead just after the half hour mark as they dominated the first half.
And Cedric van der Gun sealed victory midway through the second half.
Iron boss Adkins said: "We knew Swansea were a good side but they really demonstrated that to us.
"We wanted to play a high tempo and get in their faces - but we didn't do that.
"Our work-rate and our quality on the ball weren't sufficient - it's as simple as that."
Joe Allen shot over the bar for the visitors before ex-West Brom striker Beattie started to bully the Scunthorpe rearguard. He fired two warning shots before breaking the deadlock on 32 minutes with a stunning 30-yard free-kick.
After the break Adkins threw on substitutes Matt Sparrow and Martyn Woolford, and Sparrow headed narrowly wide.
But van der Gun fired a clinical second in the 67th minute after latching on to Darren Pratley's pass.
The Dutchman might have increased the scoreline but was booked for diving after rounding keeper Joe Murphy.
Swansea manager Paulo Sousa said: "We could have scored more but we are creating chances and I am happy with that."
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