Coach Zdenek Zeman was sacked after a poor run of results and the Stadio Olimpico outfit currently sit ninth in the Serie A table after defeat to Sampdoria on Sunday.
A number of protests have been staged outside the club's Trigoria training ground, with reports of striker Pablo Osvaldo's car being attacked by fans, but Pallotta asked the supporters to be patient with the players and coaches.
"While we are all not happy with our recent results I have complete confidence in our players and entire staff," he wrote in an official statement.
"As I have said on every occasion we are building an organisation and team that will take some time and that Rome can be proud of.
"In times of transition, there will always be instances in which, in hindsight, we may have taken some different decisions but I don't intend to put band aids on in order to satisfy some in the short term."
Directors Franco Baldini and Walter Sabatini have also been the targets of some fans, but Pallotta urged those who are unhappy at the current situation to channel their upset towards him.
He added: "I am sorry that we all would like to see quick results but since becoming president seven months ago I feel we have moved in many respects in the right direction for the longer term viability and greatness that I believe we can achieve for Roma.
"Attacking Baldini and Sabatini on a daily basis doesn’t accomplish anything and is foolish. If you want to, attack me."