After weeks of speculation the Czech tactician was finally dismissed in the wake of a 4-2 home defeat to Cagliari, with experienced coach Andreazzoli taking the reins until the end of the season.
Former France boss Laurent Blanc is one of those reportedly under consideration to be Zeman's permanent successor but Andreazzoli feels he has what it takes to turn things around.
"I'm working as if I'll be the head coach of Roma for the next three years," he said.
"I'm focusing on the future, not just looking for a quick impact in Sunday's match, although it would be good to get a result and take that energy forward.
"I want to build foundations that the club can use in the most appropriate way, with me or with someone else.
"Whatever we do will be for the benefit of the team. He who doesn't want to work that way is out - no excuses."
His first act is likely to be the recall of Dutch goalkeeper Maarten Stekelenburg, whose dissatisfaction at a lengthy spell out of the team was somewhat vindicated when Mauro Goicoechea conceded an own goal against Cagliari.
Andreazzoli should also restore Daniele De Rossi to the heart of midfield. The Italy international has spent most of the season so far in an unfamiliar defensive role.
A run of five games without a win has left Roma fans anxious for a positive display and a possible return to the European places.
Andreazzoli added: "No other club has a fanbase like Roma's, I've learned that over time.
"If we can make them understand that we are fully committed then they will always support us. I want to see the players honouring the shirt out on the pitch and just the thought of it gives me chills."
Defender Federico Balzaretti and striker Mattia Destro require late fitness tests at Sampdoria, with midfielder Panagiotis Tachtsidis serving a one-match ban.
Delio Rossi, meanwhile, has made the desired impact at Sampdoria, following up a resounding 6-0 win over Pescara with a hard-earned goalless draw at Torino.
"The real pleasure has been seeing these guys work hard," he said. "That's more important than any personal gratification and this group is completely behind me."
Midfielder Angelo Palombo and striker Maxi Lopez face late fitness tests but Rossi has an otherwise fully-fit and suspension-free squad at his disposal.