The Scottish side took a 5-0 win from the first leg of their play-off but found themselves 4-1 down before late goals from Oliver Ntcham and Leigh Griffiths eased the nerves and confirmed Brendan Rodgers' side had made it to the group stage for the second year running.
After the game, Forrest was asked who he would like to see come out of the hat in Thursday's draw. The Scotland international said: "Obviously we have had Barcelona a couple of times in the last few years so it would be nice to get Real Madrid - but we will see who we get.
"It's going to be six good games to look forward to and the full staff will be buzzing."
In the entralling encounter at the Astana Arena, the Scottish champions suffered their first defeat in 43 games, losing 4-3.
Forrest said: "I thought we did well in the first half and went in at 1-1, then conceded two goals at the start of the second-half and that kind of gave them a wee lift.
"We did it the hard way but we got there in the end.
"Qualification was an aim at the start of the season so we are delighted.
"We know when we play in Europe it is going to be difficult and you need to take your chances more than you do domestically.
"So it is a bit of a wake-up call but we are delighted to be in the Champions League."