Genoa dominated the match for long spells but Andreazzoli believes that Roma showed they possess defensive resolve to grind out a result.
He told Sky Italia: "Tonight we had the opportunity to prove that we know how to suffer under pressure and that our goalkeeper has some very useful talents.
"We held out well against a Genoa side that had got itself back on track. Roma did well to suffer when necessary, then in the second half we completely changed our tactics.
"The lads adapted and at that moment the real Roma emerged. All it needed was that everyone bring out that tiny bit more after the first half, other than Maarten Stekelenburg and Romagnoli."
The Giallorossi are now in seventh place in Serie A and four points off Europa League qualification.