The disappointment of being eliminated from the Champions League by AEK Athens last week was accompanied by a sense of anti-climax following two successive seasons at the top table.
However, Milner recognises how fine the margins can be in these qualifiers and insists that the secondary competition is by no means second rate, having captained Liverpool when they lost to Seville in the 2016 final.
“The Champions League is very tough, especially when you factor in the number of games Celtic need to play just to reach the groups,” said the 32-year-old.
“I’ve played in qualifiers before and people see some of the teams involved, with players they’ve never heard of, and they think it’s going to be easy but it hardly ever works out that way.
“You find that they’re in the qualifiers for a reason. They might not have the same exposure as the clubs from the biggest countries but these are hard ties, especially because they come so early in the season – that doesn’t make it any easier.
“Teams like AEK Athens have a lot of European experience as well. All the hard work you have done the year before to get into a position to get into the Champions League can be thrown away in a two-legged game. It is tough. European football is obviously important to a club like Celtic.
“I’m sure they’ll be pushing hard to get into the Europa League group stages – that is a great competition as well.
“Unfortunately, I lost to Seville in the final with Liverpool. Thinking about not winning that European trophy still hurts.
“There is quality in the Europa League from the start, even before the clubs from the Champions League drop in. It’s a very good tournament to do well in.”
Milner also tipped manager Brendan Rodgers to guide Celtic through the potential banana skin in the ARVI Football Arena this week, after revealing it was the prospect of working under the Irishman which persuaded him to leave Manchester City and move to Anfield in 2015.
“My impression of him is that he’s a very good manager; he was one of the main reasons I signed for Liverpool, in fact,” he said. “It’s a massive club and doesn’t need too much selling but Brendan played a very big part when I made my decision.
“From speaking with him before I joined and then working with him full time I could see how well prepared he is, how good he is tactically during training sessions and how impressive his man-management is.
“It was unfortunate I didn’t get to play under him for longer. That remains a disappointment but that’s football and it’s pleasing to me to see that he’s come to another big club and done so well.
“Liverpool’s loss has been Celtic’s gain but we were lucky enough to bring in Jurgen Klopp after Brendan. He’s another top manager so it’s worked out well for both clubs. Brendan did well at Anfield and he came so close to ending that long wait for the title.
“Would he have turned things round if he’d been given more time? I’m sure he would have done; you don’t come as close as he did to winning the league without doing something right but the club chose a different path
“But he came here and he’s won every trophy so far – he hasn’t lost a cup tie since he came to Celtic, which is ridiculous – no matter what level you’re playing at, that takes some doing.
“He’ll be a better manager now for his experience at Liverpool. The success he’s had in Scotland suggests that but Liverpool are also strong at the moment so there won’t be any regrets from either side. Brendan did a good job at Liverpool and he’s doing a good job at Parkhead.”
l James Milner was speaking to publicise A Match for Cancer which will take place at Celtic Park on Saturday, 8 September. Tickets are now on sale priced £14 for adults and £6 for concessions.