The Tigers are still reeling from Sunday's 33-0 defeat by the Irish Province in Belfast and Barnes believes the return Pool 1 fixture will come too soon for Dean Richards' once great side.
"Leicester have not been the force they were for a few years and the heart and soul of the club seems to have gone. I can't see them turning the Ulster result around," said Barnes.
"It was a great collective effort from Ulster, normally when Leicester play Neil Back dominates, but Ulster skipper Andy Ward ruled the roost in the back row and Leicester didn't seem to believe in themselves.
"However, no team in Pool 1 has won away from home and Leicester have had just one home game so far. They will feel that if they can win those two home games and triumph at The Dragons they could qualify.
"It's clear that all the teams in this Pool are far better at home than away, but the other sides will sense that Leicester are the most vulnerable side at home. If they lose to Ulster they are out of Europe, lie 10th in the Premiership and are out of the Cup. A great empire would be crumbling around itself."
|Johnson: Calling it quits?|
"It seems to be an open secret, and Leicester need him as he is as great a club man as he has been England captain," added Barnes.
"November 22 (the World Cup final) was such a big day and nothing has come easily for him since coming back. He will get over it but I don't see where he can go from here with England.
"Sir Clive Woodward's decision that all those in the Six Nations squad must be available to tour this summer may have made Johnson's mind up for him."
In Ireland, Gloucester face a stiff examination from Munster in a match which could decide the destiny of Pool 5, live on Sky Sports. It's a case of `Groundhog Day` for Barnes, the sides having met in the Pool stage last season and Gloucester having beaten the Irishmen at Kingsholm last Saturday.
"It's deja vu...Gloucester thumped Munster last season, but then got flattened in Ireland. They went over there like a football team 3-0 up, sat back and hoped it would be OK," recalled Barnes.
|Gloucester face Munster passion|
"Gloucester will bid to go out like sprinters, get a lead and hold on knowing that they will go through, probably as top seeds to the knockout stage, if they win. That would guarantee a home quarter-final, and then a semi-final in England.
"Even if they lose within seven points they will claim a vital bonus point and will have a chance to top the group."
Sale Sharks shocked Leinster Lions last week, inflicting a first-ever home Heineken Cup defeat on the Dublin-based side. Barnes expects more Irish gloom in Cheshire on Sunday - also live on Sky Sports.
|O'Driscoll: Key Leinster loss|
"Leinster are one of the favourites, Sale were not expected to compete but came through.
"With no O'Driscoll, one of the modern greats, in the Leinster side at Stockport I think Sale can win and fancy them to get through Pool 3."
The round four action begins on Friday with London Wasps going to Wales with revenge in mind after slipping up against Celtic Warriors on Sunday.
"Wasps were complacent against the Warriors, who hit them at the ruck and mauls and disrupted Robert Howley, Lawrence Dallaglio and Alex King," explained Barnes.
"There was no video referee at the Causeway Stadium so I cannot go with the controversy surrounding the winning try as the touch judge believed the corner flag was not touched and so you must say it was a good try.
"People say Wasps will not be complacent this time but Bridgend is sold out, there will be 13,000 there on Friday night and it will be new terrain for Wasps. I think it will be a lot harder than some English critics think."