Neil Lennon's side were eventually eliminated from the competition after Juventus won 5-0 on aggregate over the SPL champions to secure their place in the quarter-finals.
But their efforts in reaching the last 16 of the tournament have earned Celtic plenty of praise with a famous victory over Barcelona among other highlights.
With Celtic already cruising towards the SPL title, and the draw for the qualifying rounds of the Champions League on June 24, Forster is ready to take flight in Europe once more.
He said: "We've definitely got a taste for it now. It's been wonderful to have been involved in this run.
"We can now look back at what we've managed to achieve and I think it has been a great effort to reach the last 16.
"The big thing, of course, was getting through those two qualifying matches.
"That's the hardest bit in some ways but we earned the right to play in the group stage.
"And although over the two legs Juventus certainly deserved to go through, I also feel we still managed to play pretty well.
They showed they are a world-class outfit. Over the piece though, I think we have done everyone proud.
"It's maybe a bit too early to be thinking about next season because we now have to focus on hopefully winning the league and the Scottish Cup.
"But after this term's run, it goes without saying we'd love to do as well next season. It's something we'll all look forward to."
Meanwhile, chief executive Peter Lawwell has reassured fans the club will seek to ensure continuity despite some players "inevitably" looking to move on.
He said: "I think inevitably there will be one or two players that will probably want to move on.
"But stability is a very important thing in football so we would hope to get the balance right.
"It's been a great season so far. The Champions League has been wonderful.
"Clearly, we are not naive enough to think that people won't be recognising that.
"If he (Lennon) keeps progressing and being successful, I'm sure he will be courted at some point.
"We are hoping that he stays for a long, long time."