Edin Dzeko's goal looked to have set Roma on their way to victory against an Inter side coached by former boss Luciano Spalletti, but Mauro Icardi's brace and Matias Vecino's clinching strike turned the game on its head late in the second half.
And while Di Francesco conceded that his team should have been more clinical, he was pleased with the performance in a disappointing reverse.
"The fact remains that, for 70 minutes, Roma were not just good but great," he told Mediaset Premium.
"We were fantastic in every way. We kept pressing to win possession back in their half and caused all sorts of problems.
"We should have been more clinical and finished more of the chances that we managed to create. Inevitably, though, with the lack of a genuine right-back, our moves were a little lopsided.
"It's a pity about the result – I know the media will only look at that – but I have to examine the performance. I saw definite steps forward.
"If there was one team that deserved to win and have a two-goal advantage, it was Roma and that's all there is to it."