Duggan was celebrating City???s FA Women???s Cup quarter-final win over Birmingham with team-mates Izzy Christiansen and Michelle Hinnigan at Wing???s restaurant in Manchester when the group bumped into United boss van Gaal.
The 23-year-old, who joined City from Everton in 2013, and who has also made 16 appearances for England, was subjected to abuse on social media after her posting, which was subsequently deleted.
Duggan said: “I would like to apologise to all MCFC fans for the error of judgement I made last night.
“I now appreciate the significance of my actions and can assure everyone connected with Manchester City that I am proud to represent the club and wear the shirt.”
Duggan has just returned to action following a knee injury which forced her to miss England???s prestige friendly with USA and the Cyprus Cup triumph last month.
The forward??scored the opener in City???s 3-1 win over Birmingham on Sunday. City now face Chelsea on May 3 for a place in this year???s historic FA Women???s Cup final at Wembley.