The on-loan midfielder is currently suspended from domestic league games as part of a 12-match sanction by the English Football Association following the fall-out from his sending-off in QPR's final match of last season at Manchester City.
However, Barton, 30, can still play in European ties and made his debut for the French side in their Group C opener away to Fenerbache, which finished 2-2.
"I see these games mostly as an opportunity to play, to have more time in the field, and so get better physically," Barton told the club's website, www.om.net.
"Because of this break due to my suspension, every game is a little Christmas. I am impatient, and I am counting the days before Limassol."
Marseille coach Elie Baup warned his squad must quickly regroup following their 4-1 defeat at Valenciennes, which brought Marseille's 100% start to the new domestic season to an abrupt halt.
"We are going to talk things over, and work. We mustn't get too bogged down in a heavy defeat like this one," said Baup, whose side host rivals Paris Saint-Germain on Sunday evening.
"We have to quickly refocus on what is coming, and get ourselves turned round."
AEL may be debutants in European group stages, having lost to Anderlecht in the Champions League play-offs, but will be looking to emulate the success of APOEL who caused an upset last season when they dumped Lyon out of the Champions League to reach the quarter-finals.
Goalkeeper Matias Degra conceded only 10 goals in 32 games as AEL won their first domestic league title since 1968.
Degra returned a clean sheet in the Group C opener against Borussia Monchengladbach, which finished 0-0 at GSP Stadium, Nicosia.
The 29-year-old Argentine, however, knows their European adventure represents a step up in class.
"This competition is a great experience for us. All our opponents are difficult so we just need to take every game as it comes," he told www.uefa.com.
"The fact that the other game [Marseille against Fenerbache SK] ended in a draw means that, essentially, we all start from the beginning again so that's a positive.
"Let's hope we can get something out of this game too."