Di Francesco abandoned the 4-5-1 shape he used in the 4-1 first-leg defeat by Barca at the Nou Camp, instead engineering a 3-5-2 formation which saw his side overwhelm the Liga leaders with relentless high pressing and long balls behind the defence.
"We had a long way to go after the first leg but all credit to the coach because he invented this formation two days ago, he drilled it into our heads and it worked wonders," midfielder De Rossi told reporters after Roma went through on away goals.
De Rossi hammered in the second goal of the night from the penalty spot after Edin Dzeko had got the hosts off to the perfect start by opening the scoring after six minutes at an electric Olympic Stadium.
Greek defender Kostas Manolas headed home the crucial third goal from a corner with eight minutes remaining, joining De Rossi in making up for scoring in his own net in the first leg of the quarter-final tie.
Dzeko also waxed lyrical about his side's tactics and said he played with more freedom alongside Patrik Schick in attack, with Radja Nainggolan, who missed the first leg with injury, behind them.
"I have never seen Barcelona struggle so much, we pressed them throughout the game from the first minute, Dzeko said.
"It was easier for me to play when Schick and Radja were closer to me, it created more space and stretched their defence. It was (also) the first time we played with three at the back and we did great."
As well as scoring the first goal, Dzeko won the penalty which De Rossi converted, having been hauled to the floor by Gerard Pique, and it was also the Bosnian who had struck Roma's crucial away goal at the Nou Camp.
"We all believed, even if everyone else gave us a five per cent chance," Dzeko added. "Tonight we proved we can play against anyone, as Barcelona are such a strong side. We put three goals past them and we could have scored more."
Di Francesco said the aim of the change in formation was to make his side more dangerous down the flanks and also praised his players for their near-perfect display.
"I made this choice to give us more width, allow us to have more counter-attacks and bring us more pace but what really changed was the philosophy of the side," he said.
"I take the blame for defeats and some ungrateful words on social media, so I may as well take the credit for a win." (Reporting by Richard Martin; editing by Ken Ferris)
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