Celtic's nerves were eased by goals in the 80th minute from Olivier Ntcham and Leigh Griffiths in the last minute of regulation time.
Celtic finished bottom of a group topped by Barcelona last season, having also met the Catalans on Champions League duty in 2013, 2012, 2008 and 2004.
"I thought we were going to get through this campaign without the anxiety but that little period they scored two quick goals, we were working on the side to plug gaps".
"But we look forward to the draw".
"Captain Brown added: "[We were] not so good coming over here, 4-3 was an exciting game for the neutral but not so much for us.
"I am very happy and pleased to come though the six qualification games, especially against a team like Astana who are a good side".
The top two in each group qualify for the Champions League second round, with third place entering the Europa League knockout rounds. "I think it's absolutely brilliant for Glasgow, the city because it's not just about the football, it's about the nation - what it does economically, commercially, what it brings into the city of Glasgow, Champions League football, businesses and everything".
Brendan Rodgers' side were given a scare by Kazakhstan side Astana in the week but there has been no nightmares in the league so far for the Hoops. "They threw everything at it, they changed their shape". Then, almost 20 minutes before the end of the match the stadium got ecstatic again as Patrick Twumasi produced another masterpiece, getting through and beating the goalkeeper. The score was 4:2 ten minutes before the end of the match.
"I have always said that I can only do my best for Celtic and hopefully that worldwide (call-up) will come". We've been prepping at tBB towers by taking a leaf from our friends over at Cartilage Free Captain, who have been using this nifty tool to work out exactly how bad things could get if the draw goes wrong. "We want to start well at home".