The capital club are now level on points with arch rivals Lazio, but ahead on goal difference.
Roma drew 1-1 with Udinese last weekend, but Andreazzoli said that his team made a "great step forward" last night.
The 59-year-old took the time to praise his captain Totti, whose 226th goal means that he is now alone in second on the list of all-time top scorers in Serie A history.
"I am satisfied with the performance, as we made a great step forward," Football Italia quotes Andreazzoli as saying. "We prepared for this game and applied our plans consistently.
"Of course, with Totti playing at this level, then it all becomes easier. He makes even the most difficult moves seem simple.
"We have a very precise idea of how to contribute to the attacking moves. Last week I said we were inconsistent, but today I saw that development."
Roma travel to Palermo for their next fixture after the international break.