Neil Lennon's side enjoyed a memorable European adventure last season, with a famous victory over Barcelona helping them into the last 16.
Matching, or bettering, that achievement is now the challenge facing all of those at Parkhead - on the back of another SPL title success.
Matthews believes the Hoops should be gracing the latter stages of continental competition, but appreciates that they can take nothing for granted after being handed a tie against Northern Irish outfit Cliftonville in the second qualifying round.
He said in the Daily Record: "We've got to respect them and treat it like a Champions League game. We want to be in the group stage every season.
"That's our main goal so we'll play every game like we're up against Barcelona again or Juventus in the last 16.
"We want to get to the group stage again as we know we need to be playing at that level. We showed last season we can compete with the best teams.
"I know Cliftonville won their league comfortably. They're going to be a decent outfit and probably a good footballing team.
"We're focused on ourselves, we only had a short break so everyone has come back in good shape."