Olivier Ntcham's stoppage-time winner in the Stadio Olimpico kept the Hoops top of Group E and ensured European football after Christmas with two fixtures remaining.
The Scottish champions' first win on Italian soil after 13 attempts left them with 10 points from four games after a draw in Rennes, a victory over Cluj at Parkhead and home and away wins over the Serie A side.
Forster, in his second spell at Celtic after joining on-loan from Southampton for the season, believes their Europa League form has been consistently good.
The 31-year-old said: "It is fantastic. Real credit to the lads.
"From that very first game we showed what we can do and played the way we know we can play.
"It is fantastic to qualify out of the group already. Absolutely amazing, fantastic result.
"The circumstances and the way we did it, just makes it that bit more special.
"No Celtic team had won in Italy before so it is an amazing achievement and fantastic to qualify out the group already."
Forster now wants Celtic to make sure they finish top of Group E in their final two matches, at home to Rennes and way to Cluj.
Ahead of Sunday's visit of Motherwell in the Ladbrokes Premiership, the England international said: "That is obviously what we are going to aim for now. That's the main thing.
"We have done well to this point but we want to finish strong and yes hopefully go on and win the group.
"We want to go on and win the group first and foremost and then we will park that for a bit and then carry on in the Europa League after Christmas.
"We are not looking too far ahead, taking it game by game and we will see where it takes us."
Not for the first time this season, Forster, sidelined at Southampton for around 18 months, revealed his delight at being back at Celtic and involved in big European nights.
He said: "It is amazing. You can't describe the feeling you get from playing in games like that one, the places you come and play.
"For me it is fantastic.
"Something that I have really missed, something that I have really cherished.
"It is a real honour to play for this club and play in these games."