The U’s fell behind to Jefferson Montero’s clever back-heeled finish, but rallied impressively to run out 3-2 winners.
It was not an upset rooted in soaking up pressure and making the most of good fortune when they got forward.
By contrast, the underdogs had more shots on target and almost twice as many corners as their illustrious visitors.
Appleton was full of pride for the way his United side performed and thought no-one could argue the best side won.
He said: “I like to think so and it would be hard to disagree with that.
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“That’s the most pleasing thing. Sometimes you can dig in, get ten men behind the ball and hit teams on the break every now and again.
“But the reality is we came here and wanted to have a right go.
“We did that and our play was there for everyone to see – it was very good.”
It was not the first shock Appleton has engineered as a manager.
His Blackburn Rovers side won 1-0 at Arsenal three seasons ago, but it was pulled off in very different circumstances.
He said: “When I went to the Emirates we defended for our lives and put ten men behind the ball to see what we could get.
“Here we went for them and I thought we should have been going into the break two or three goals up.
“The style of play topped everything off for me.
“It’s up there as one of my best days as a manager, definitely. Hopefully there’s more.”
He added: “We knew we would have an opportunity if we stuck to what we know best.
“I like to think we passed the ball well and we pressed as high as we could when we got the opportunity.
“I think it unsettled them at times.”
While Appleton named an unchanged side, Swansea made ten changes.
Manager Alan Curtis still felt a side containing four senior internationals was strong enough to go through, but had no complaints about the res-ult.
He said: “All credit must go to Oxford, I thought they were excellent.
“They were much more energetic, they passed the ball and were the better side overall.”