Despite the numerical disadvantage, it was Ulster who led 9-5 at the break, courtesy of three Ruan Pienaar penalties, with Chris Ashton's try the only score for the current English Premiership leaders.
And while Ashton would touch down again, as well as Mouritz Botha, Saracens were never out of sight with two late Paddy Jackson penalties making for a frantic finish.
It left Muller proud of his troops, with the South African believing the performance served to highlight the character of the team.
"I can't be prouder of that group of players," Muller said. "To play for 75 minutes with 14 [men], and to get within two points of winning and losing is an unbelievable achievement.
"The passion and the commitment the boys showed out there, just shows the quality of this side. Like I said I can't be prouder of them.
"It all comes down to one thing and that's character. It would have been easy to go after ten minutes, 'we're never going to win this game,' the easiest thing is to lie down and give it to them but I think the true character of this Ulster side came out and we really gave it 100 per cent for the game."
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