The 3-2 victory, thanks to a late header from Georgios Samaras, was the Hoops' first triumph away from Parkhead in the group stage of the competition and left the Scottish champions second in Group G behind Barcelona with four points from two games. However, the Celtic midfielder is aware that next up in Europe is a double-header against the Catalan giants.
"We are just happy to be in the competition," Ledley said.
"We are enjoying every minute of it but we don't want to say that we are going to qualify."
"We have two games against Barcelona which is fantastic for the players but it will be very difficult."
"You never know. Hopefully we can get a win or a couple of points, but we will take it game by game and see how it goes."
"We are talking about the best players in the world so it is going to be very difficult but we are happy with the four points out of six at the moment."
Ledley was at Hampden yesterday for the Scottish Communities League Cup quarter-final draw, where Celtic were handed a home tie against St Johnstone, who beat Neil Lennon's men at McDiarmid Park in the league last month. The former Cardiff City player said:
"It is a difficult draw. They have beaten us already this season so we need to perform better against them the next time."
"But we are just happy that we are home."
While there appeared to be some disappointment that Celtic and Rangers had avoided each other - the Ibrox club were drawn at home to Inverness - Ledley said:
"Maybe if we get through we can play them another time."