Brazil international star Alisson joined Premier League side Liverpool in a deal that could earn Roma up to £65 million (€73m/$85m).
Former attacker Totti, however, admitted Roma could not say no to the money on offer despite Alisson's quality.
"We're building a young team for the future," Totti told Sky Sports Italia .
"We'll try to strengthen as soon as possible, so that Roma can compete at the top.
"Alisson? The market figures have changed, €75m for a goalkeeper happened for the first time and we couldn't say 'no'.
"I'm sorry that we've lost one of the best goalkeepers in the world, but we'll try to build a strong team regardless."
Alisson is not in Liverpool's squad for their International Champions Cup campaign in the United States following his World Cup commitments with Brazil.