The former Gers and Scotland striker, who scored a club-record 355 goals during his 15-year stay at Ibrox, believes the pressure is on both sides to get off the mark in their respective groups.
McCoist knows Celtic will start as underdogs despite playing in front of their own supporters at Parkhead but is unsure if the current Leverkusen side are of the same quality to the team that comfortable saw off Rangers over two legs in the Round of 16 during the 2019/20 season.
Speaking on talkSPORT, he said: “Both teams have got to take something after the disappointment of the opening games.
“Celtic were unlucky – to go to Real Betis and score three goals, you expect to get something.
“To be honest, Rangers were beaten by a better side in Lyon, they definitely were.
“I don’t think Leverkusen – and I might be wrong – are of the quality they were. I saw them a few years back and they were just too good for Rangers.
“They had Kai Havertz and they were just a proper team. I’m not sure they’re just of that quality now.
“I think both Rangers and Celtic could seriously do with something tonight.”
McCoist will join the BT Sport punditry line-up this evening alongside Derek McInnes and presenter Darrell Currie to provide analysis on Rangers clash with Sparta Prague, with Rory Hamilton and Alex Rae on commentary duty from the Letna Stadion.
Paul Lambert and Neil Lennon will then step in to analyse Celtic’s match against Bayer Leverkusen, with Chris Sutton joining Rob McLean in the commentary box at Parkhead.