Stekelenburg flew from Italy to London on transfer deadline day in anticipation of a switch to the Premier League being completed, only to be told the move was off.
The Dutchman has slipped down the pecking order at the Stadio Olimpico, with Mauro Goicoechea established as the No.1 for the Serie A side.
Cottagers boss Martin Jol, who knows the 30-year-old from their time together at Ajax, was hoping to bring in a long-term replacement for veteran Australian Mark Schwarzer, who will be 41 later this year.
Stekelenburg said he was flying to London when his agent Rob Jansen informed him the move was off because Roma could not agree terms with Fiorentina's Emiliano Viviano.
The keeper told sportpromotion.nl: "This feels like a major setback in many ways. I was really looking forward to getting started at Fulham.
"It is a great club and it would be an understatement to say the league is great too. It is a blow and I will need time to process it."
The former Ajax man has publicly voiced his frustration at losing his place to Goicoechea but refused to hold Roma accountable for Thursday's events.
"I can't really blame anyone in this situation," he added. "Roma made it clear from the outset that they would only sell me if they could bring in an adequate substitute.
"My agent Rob Jansen and I were informed that the clubs were in agreement with each other.
"We were there in person to meet Fulham so the wait was purely over my replacement in Rome. But they didn't find one and that's the reality.
"My first challenge is getting my place back at Roma, then we'll see how things stand in the summer."
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