Scotty’s got a clear head
hauled Fulham level with a fine strike 10 minutes after the restart.
Macauley Bonne’s header put the visitors back in front two minutes later before but Aleksandar Mitrovic smashed home from close range in the 63rd minute as Fulham levelled again.
Bobby Decordova-Reid and Mitrovic both came close to a winner, but Charlton survived the onslaught to claim a point.
Parker added: “I’m probably a little bit disappointed we’ve not come out of this one winners in the end.
“I thought they caused us problems in the first half and were worthy of a one-goal lead. The game was pretty stretched and we looked like we lacked a little bit of energy.
“But second half we changed it around and we had a couple of glorious chances and the keeper has pulled off a world-class save.”
Charlton chief Lee Bowyer hailed teenage midfielder Gallagher, who scored his fourth goal since his summer switch from Stamford Bridge.
Bowyer said: “He’s surprised me, but I think he’s surprised everyone.
“He’s surprising Chelsea as well as they didn’t know how far he could go.
“For a 19-year-old kid who hasn’t played men’s football before, Chelsea are delighted with him.”
CHARLTON 7 ........ Shots on Target ......... 5 9 ........ Shots off Target ......... 3 8 ................Corners ................. 6 12 ................. Fouls ................... 14 1 ................ Offsides .................. 1 83.3 . Passing Success % ... 60.9 528....... Total Passes ......... 233 69.9..... Possession % .......30.1 52.3..Territorial Adv % ... 47.7