City have failed to reach the last 16 in their previous two campaigns after being given tough groups, but the latest draw in Monaco looks to have been kinder on new manager Manuel Pellegrini.
They have been placed in Group D with holders Bayern Munich, along with CSKA Moscow of Russia and Czech side Viktoria Plzen.
Asked about facing Bayern, Begiristain told Sky Sports News: "They won three trophies last season so of course they will be very strong, but already this summer we have played a friendly and now we have the real competition."
CSKA came out of the second pot of seeds and will be considered City's main rivals for a top-two finish alongside favourites Bayern, but Begiristain is not taking Plzen for granted either.
Questioned on whether the two clashes with CSKA may prove decisive, he said: "We have to be careful of Viktoria Plzen also and respectful of all the teams.
"They (CSKA) are the champions of the Russia league and are doing well. They have a good team with some good players and it will be difficult, but we have a lot of confidence this season.
"We have improved the team, we have a new manager with a lot of experience in the Champions League and we hope we will be stronger in the Champions League."