The eight-year-old was with her family when suicide bomber Salman Abedi detonated a home-made device, killing 22 people including seven children.
Following a concert in Buenos Aires on Wednesday, the singer tweeted, "Saffie, we're (thinking) of you baby" alongside a birthday cake emoji.
The youngster, from Leyland, Lancashire, would have celebrated her ninth birthday on July 4.
To mark the occasion her family chose to speak out, paying tribute to Saffie and remembering how she had looked forward to the concert.
Her older sister, Ashlee Bromwich, said the super fan was "elated" as she watched her idol on perform on May 22.
"She was Ariana Grande-obsessed, so to see how happy she was, it was just ... obviously I had to go with her," she told the BBC.
Her father, Andrew Roussos, said: "You couldn't be out with Saffie without having fun, but her dream was to be famous. It was her everything and we bought her the tickets for Christmas.
"She was just counting the days, the seconds and it was just Ariana Grande until nine, 10 o'clock at night. And she would sing and dance every single song."
The explosion ripped through the arena foyer as thousands of fans, mostly young girls, left the venue following Grande's performance.
Mr Roussos, who said "all hell broke loose" after the bombing, was later told by a police detective that Saffie had died.
"We've lost everything. We have, we've lost everything, because life will just never be the same," he said.