The Clydesdale Bank Premier League champions dominated possession after going behind in eight minutes to Hibees' on-loan striker Leigh Griffiths' 14th goal of the season.
However, it proved to be frustrating afternoon for Neil Lennon's men as they failed to find a way past a resolute Leith defence.
Lustig, though, can point to the fact the Hoops remain six points clear of Inverness at the top of the SPL table with a game in hand, still in both domestic cup competitions and with a Champions League last-16 clash with Italian giants Juventus next year to relish.
The Sweden full-back wants Celtic to start off 2013 by returning to winning ways against the Steelmen at Parkhead.
He said: "We are a big team in Scotland and of course we want to win every game but if we lose a game we are still the same players who have done very well this season so far.
"So hopefully we can play a good game against Motherwell, score some goals and get back on track.
"I think we were the better team against Hibs but that's football and if you don't score it is hard to win. The attitude and character we showed was brilliant at times.
"But we are Celtic players and we don't like to lose, we always want to win. We always think we should score goals.
"I think we created some big chances and had some good crosses and as I said before, goals are really important."