The Hoops started their campaign with a 3-0 win over Cliftonville in the first-leg of their qualifier in Belfast on Wednesday night.
Goals from Mikael Lustig, Georgios Samaras and James Forrest gave Celtic a commanding lead, but they were without injured trio Charlie Mulgrew, Adam Matthews and Joe Ledley, while star striker Gary Hooper has been linked with a move away.
The arrival of new recruits Amido Balde, Virgil Van Dijk and Steven Mouyokolo have strengthened the squad, but Commons believes two or three signings are still needed to ensure the team can reach the group stages.
"We will pick up injuries throughout the season so it is important that people that are pushing us all the way are more than capable of playing at that sort of level," he said.
"So it would be ideal if we could get two or three good additions to maintain that level.
"We are always trying to improve, we want to make the group stages of the Champions League and obviously we have three (domestic) trophies to win this season."
Celtic were given strong support at Cliftonville and Commons felt the night was yet another reminder of the Scottish champions' "worldwide" status.
"Wherever we have been in Europe, our travelling support has been incredible," he said.
"Even the time when we went to Australia for pre-season, there was support down there.
"We are playing for a club that is worldwide. We have a lot to live up to.
"When you pull on that shirt, you know you are representing a club that is worldwide and that is something you take great pride in."