The Giallorossi leapfrogged Napoli into fifth place with a 3-1 triumph over Udinese on Wednesday and take on Fiorentina in Rome on Sunday.
That result followed their 4-2 defeat at Lecce and allowed Roma to close the gap on third-placed city rivals Lazio to four points.
The top three teams in Serie A qualify for Champions League football next season.
"We were really determined to put behind us our dreadful performance against Lecce," Totti said. "We played very well against Udinese and this is the way we must play our remaining games.
"Our aim is still to finish third and we will give everything we have to win all of our remaining games."
Roma, coached by Luis Enrique, will fancy their chances after winning five of their last six league games at the Stadio Olimpico.
However, they can expect a tough battle as Fiorentina are looking to take a step towards Serie A survival.
The Tuscan outfit were held to a goalless draw by Palermo in midweek and are in 16th place, just three points above the drop zone.
"We are taking it one game at a time," Fiorentina defender Manuel Pasqual said. "We know we face six finals and we cannot afford to make mistakes. We will go to Rome determined to take home a good result."
The visitors will be without suspended striker Carvalho Amauri. Adem Ljajic will play in support of Fiorentina's top scorer Stevan Jovetic.
Roma striker Fabio Borini has shaken off a muscular injury that kept him out of action for the last two weeks and will feature on Sunday.