"To get our first Champions League win away and to keep a clean sheet, the first in so many years, is really pleasing".
Striker Griffiths lit up a tiresome first half at the Constant Vanden Stock Stadium with a poacher's goal from Kieran Tierney's 38th minute delivery and, five minutes after the break, Roberts' drive took a deflection in off substitute Kara Mbodji.
With Bayern Munich and Paris Saint-Germain being the undisputed favorites to advance from Group B, goals by Leigh Griffiths and Scott Sinclair, along with an own-goal by Kara Mbodji, gave the Scottish champion an important victory.
There were a total of 28 passes between the Celtic players, with a great cross in from Kieran Tierney to his Scottish global teammate Griffiths, who provided the finish. "That's something I said to the players afterwards that we need to continue to work on because at this level you have to be that little bit more patient also".More news: Keeper Karius to start for Liverpool against Spartak Moscow
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And it got better for the travelling supporters when Roberts' deflected strike fired the Bhoys 2-0 up after a mistake at the back from Leander Dendoncker.
"In spells with the ball we were very, very good".
Anderlecht's interim boss Nicolas Frutos stood on the sidelines frustrated as Rodgers' side withstood everything the Belgian champions could throw at them before Sinclair scored a breakaway third in added time.
Despite Celtic being strong domestically, their Champions League form has been poor and they were defeated 5-0 by PSG two weeks ago. What can be said with confidence is that the manner of the win in Belgium has instilled fresh belief into a squad which remains relatively inexperienced in Champions League terms. The boys deserve a great amount of credit for the performance.