Roma, who visit Napoli in Serie A on Sunday, quickly played down Totti's comments which followed criticism of his missed penalty in last Monday's 1-1 draw at home to Juventus.
Sporting manager Walter Sabatini praised Totti for showing his emotion and said the 35-year-old's comments were made in the heat of the moment.
"I don't like calm waters, he has been hurt by the criticism," he told Sky Sports Italia. "He has been spontaneous and has done the right thing by saying it.
"Totti's not going anywhere, he is Roma," Sabatini added. "He will continue to represent Roma for many years."
Totti, who has often been relegated to the substitutes' bench by coach Luis Enrique, said: "If I'm the problem, then I'll think about [leaving].
"It's not because of the club or the coach or my team mates, I dislike things a few fans have said against me.
"If things carry on in this way, I will continue to think about it."
Roma, taken over in April by a consortium led by United States businessman Thomas DiBenedetto, have struggled to live up to expectations which were heightened by a summer spending spree and Luis Enrique's comment that he wanted them to play like Barcelona.
Instead, they have managed five wins in 14 Serie A outings, dropping to 10th with 18 points and 12 behind leaders Juventus.
Luis Enrique, who took over in the close-season, quickly courted controversy by leaving Totti on the bench and the storm only subsided after the striker issued a statement asking for backing for the coach.
There was further trouble when leading scorer Pablo Osvaldo lashed out at teenager Erik Lamela after a match at Udinese and was suspended for one game by the club.
Under pressure Luis Enrique, whose future has already been questioned, then lost his temper and swore at journalists in a media conference before the Juventus game.
Unbeaten Juventus, level at the top on 30 points with surprise package Udinese, have a chance to go clear when they host Novara while their rivals have a much more difficult match at Lazio.
Lazio, winners of their last two games, are level on 28 points in third place with AC Milan, who should win at home to a Siena team who have taken one point from their last 15 and are only two points above the relegation zone.
Inter Milan, who climbed from 15th to sixth after two wins in the last week, host a Cesena side who were winless in their first 10 outings but have won three of their last four.
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