That now looks unlikely as they remain six points behind the Londoners in seventh with two games left.
The 40-year-old Welshman's side huffed and puffed in search of an equaliser to Sebastian Larsson's goal but never really looked dangerous, especially with Wayne Rooney missing through illness and injury.
Giggs, still registered as a player at the club where he has won every honour in club football, sent on Robin van Persie, Danny Welbeck and Adnam Januzaj after the break, all to no avail.
"The players were a bit flat, why I don't know," Giggs said.
"We controlled the game but lacked that bit of quality in the final third."
Giggs said he might even consider picking himself for Tuesday's game against Hull City.
"I'll train over the next few days and if I'm fit enough I'll play," he said.