Chelsea were defeated last season by an injury-time Andres Iniesta goal in their semi-final against eventual champions Barcelona.
"We start again and are always looking to get one step further," said Chelsea chief executive Peter Kenyon after Thursday's draw in Monaco.
"There are no easy games or groups but overall not too much travel and we have managed to avoid one of the big ones."
Manchester United will return to CSKA's Luzhniki Stadium, where they beat Chelsea in the 2008 final, and chief executive David Gill said: "Overall we have got to be happy with our draw.
"We are looking forward to going back to Moscow after those great scenes in 2008."
However, boss Sir Alex Ferguson played down his side's chances, telling the club's website: "These are difficult ties, especially the trips to Russia and Turkey.
Manchester United will return to the site of their 2008 title win
"CSKA have developed strongly in the last few years, and games in Turkey are always difficult.
"We also know the quality that we're up against with Wolfsburg, with what they achieved in the Bundesliga last season."
By contrast, Liverpool managing director Christian Purslow said his club were "pretty happy" with their group.
"We have two very well-known European opponents, who will not bring us any surprises," he said.
Reds legend and club ambassador Kenny Dalglish added: "It could have been worse but it could have been easier as well.
"You never dismiss Italians - they will be well-organised and very effective, and Lyon have had great success in this competition."
Arsenal chief executive Ivan Gazidis was also wary about the opposition his side face in Group H.
"Some might look at it and see it as an automatic pass but we don't see it like that," Gazidis said.
"We think it will be very tough. But we won't lose our focus. We have a very determined group."
Rangers, in pot two, could have faced any of the English clubs but appear to have been handed a relatively favourable draw that includes the unknown quantity of Unirea Urziceni.
The Romanian side, along with Wolfsburg, Rubin Kazan, AZ Alkmaar, Standard Liege, Debrecen, APOEL Nicosia and FC Zurich, make their Champions League debut in this year's tournament.
Gers chief executive Martin Bain said: "It's a good group. Sevilla are Uefa Cup winners twice in the last five years.
"Stuttgart have now qualified for the Champions League three times and each time have been drawn to face Rangers.
"We beat them at Ibrox and lost in Germany on both occasions, so hopefully we can go one better this time."
There are 32 teams left in the competition, split into eight groups of four, with the first matches to be played on 15/16 September.
United, Liverpool, Chelsea and Rangers all reached the first round automatically, while Arsenal eased to a 5-1 aggregate victory over Celtic in qualifying to clinch their place in the lucrative stages of Europe's premier competition.
The eight group winners plus the runners-up go through to the knockout stages of the competition, while the teams finishing third go into the Europa League.
Real Madrid's Bernabeu Stadium will stage the Champions League final on Saturday, 22 May 2010.
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