Roy Keane claims Celtic should be setting their sights higher in Europe following their 7-0 thrashing by Barcelona.
Celtic boss Brendan Rodgers argued the Camp Nou loss was no embarrassment, but Keane feels his former club's mindset needs to change in European competition.
The former Celtic midfielder -- who rejected the chance to manage the club in 2014 -- was disappointed with the way they celebrated their Champions League qualification following a 5-4 aggregate win over Israel's Hapoel Be'er Sheva.
After watching a Rodgers interview, Keane told ITV's Champions League highlights programme: "I know it's difficult after a game, and if you have an off night in Barcelona you are in big trouble. But on one hand we are being told that Celtic are a great club, great traditions, great history and they go and lose 7-0 to Barcelona and people almost say, 'Well these things happen, it's acceptable.'
"He spoke about the game the previous week against Rangers. They won 5-1 against one of the worst Rangers teams I have seen in a long time, who finished with 10 men for the last 15-20 minutes. So that idea they were tired as well....
"All I hear sometimes when people talk about Celtic is about winning the league, but I think they need to do a lot better in Europe. It's easier said than done of course and this time round it's obviously difficult with the group they are in.
"But even in the qualifying games they were poor. They scraped through and didn't win any of their away games. I think the whole mindset has to change and don't accept, particularly away from home, being the whipping boys of Europe."
Celtic overturned a first-leg defeat against Gibraltar's Lincoln Red Imps in their opening qualifier before beating Astana 2-1 on aggregate to set up the Israeli challenge.
Republic of Ireland assistant manager Keane added: "It's Celtic, a huge club, and they need to do a lot better. Even when they qualified for this group the celebrations were way over the top. They scraped through and I thought they'd actually won the competition. People were hugging each other -- the manager, the coaches, the players. They should be expecting to do well in this group.
"Throughout the last number of years when they have been involved in Europe they have struggled and lesser teams than Celtic have done well in Europe.
"A lot of these players for Celtic are international players. It's not Altrincham, it's Celtic. They've got to do much better."
Former Celtic striker Jan Venegoor of Hesselink said Celtic's players should not find it too hard to discard the effects of their 7-0 thrashing
The Dutchman, who played for Celtic between 2006 and 2009, believes Rodgers' players will be able to put the defeat into context.
"Sometimes you put your hands up and say they were a much better team, learn from it and move on," he said. "If it is another team, with all due to respect to a team like Borussia Monchengladbach or someone, but this is Barcelona, one of the best teams in the world with some of the best players in the world.
"If you miss the penalty it is going to be really hard. Maybe if you score the penalty you can sit back a little bit but they just play football from another planet some times. So I think this is not hard for the players to let go.
"Of course, the players and the manager will speak about that and show tapes and say you need to do this and that but sometimes you need to put your hands up.
"If you look at the first goal for Messi, or the fourth or fifth goal, you can put any player there and you can't stop those types of players and so I don't think they will be bothered about it too long."
Celtic get the chance to make amends against Inverness on Sunday where they look to cement their place at the top of the Premiership, where they have won their first four games.
Venegoor of Hesselink, appearing with former Rangers defender Arthur Numan at a William Hill media event at Ayr Racecourse where they made the draw for the William Hill Ayr Gold Cup race on Saturday, said: "That is the good thing about football.
"On Saturday it was the biggest high and on Tuesday night they were at the lowest point and now the next game you can show that you are capable of winning the league.
"You can turn things around really quickly and make sure you win the game so no one can hold it against you."
In the other Group C game, Manchester City beat Borussia Monchengladbach 4-0 at the Etihad stadium.
Despite such a convincing defeat for the Bundesliga outfit, Venegoor of Hesselink believes Celtic have got a job to finish third in the section and qualify for the Europa League.
He said: "It is going to be a big task. They are a really good team, a Bundesliga team and I watched them play earlier this year but City are on a high.
"You need to have everything with you and you need to produce, especially in home games because anything can happen in home games, as Celtic have showed it in the past.
"Like I said it is a Bundesliga team and the Bundesliga league is really strong. I think they can still get third but you need to be a little bit lucky."