The removal of the Gers as direct competition has reduced the prestige of domestic honours.
The Norwegian clinched the league title and league cup in his debut season, but the absence of Rangers as a real force has made domestic honours an expected, rather than impressive, achievement.
Pressure to deliver in Europe has increased as a result and it’s on this stage where Deila has so far come up short.
The Hoops have missed out on Champions League qualification in successive seasons at the hands of Maribor and Malmo – and were beaten in their last Europa League group game by Molde - and McLeish feels Celtic need to overcome teams of that calibre.
“I’m not going to speculate on Ronny’s future but he has got to beat these teams. At Celtic your spending power is probably bigger than theirs,” said the former Gers boss, in an interview with the Daily Record.
“So is it then an indictment on the Scottish league that the Swedish league is better? That it is more competitive for Malmo. Is it more competitive in Norway for Molde?
“These are the hurdles Celtic have to get over, starting in the next home game. I think Ronny has to be beating these teams. I’m not trying to put pressure on him. I just know, having been there as a manager, that would be the same expectation for me,” he added.
Rangers’ expected return to the top flight next season will breathe new life into the domestic challenge but until then, the pressure is on Deila’s shoulders to deliver in Europe.
Celtic sit bottom of Group A after three games and will need to beat Molde at Parkhead next Thursday if they are to have any realistic chance of qualifying.