With City's squad one of the most expensive to have been assembled in Europe, many pundits have suggested that Manuel Pellegrini's side should be making a major impact on the tournament.
However, having collected just one point from a possible six in the group stages, Zabaleta has revealed that lifting the famous trophy is not a part of the squad's current thinking.
"We're not thinking about [winning the Champions League]. Sometimes it takes time. We know we are a team, a club that have been improving the last few years but the Champions League demands much. We are improving year by year but to win the competition is difficult," he told reporters.
City take on CSKA Moscow on matchday three in Russia tomorrow evening.