The Warriors open their bid to stop that run with a home tie in Round 1 against Newport Gwent Dragons and will also be up against defending champions Toulouse and former champions London Wasps in a strong Pool 6.
They will be without points machine Dan Parks, who went south to the Cardiff Blues in the summer, but Kellock believes they have the youngsters to step up and fill the gap.
"Dan is a great player and would be a loss to any team but, saying that, the two young guys at 10 - Ruaridh Jackson and Duncan Weir - are real stars," said Kellock.
"They both have great attitudes and I'm excited about them. But the things that have gone wrong are not down to the guys that have come in, they are team things. If we can get that sorted out then I believe we will start to win games.
"It's good to have a home game first and we know the Dragons pretty well from both the Celtic League and the Heineken Cup in the last couple of years.
"Hopefully that will be positive for us because we are definitely looking to put one over them.
"The recent league match against the Dragons was a really tough game, it was extremely physical, and they have a big and direct pack. All credit to them as on the day they played well.
"But it has been shown in past years that league results mean very little when it comes to the Heineken Cup so we will be looking forward in a positive manner to the game.
"It's a tough start but the attitude of the players has been excellent and we have made silly mistakes and teams have punished us.
"A big positive from last year was we were winning the tight games and we weren't giving anything away cheaply.
"We have shown over the last few years that we can be competitive so we know the challenge is to prove we can also be consistent.
"There is no point winning the big games and then losing a couple. We have to push on and get to the final stages. Every team in the tournament will first of all target getting out of the group and qualifying for the quarter-finals.
"We are no different and if we play to the best of our ability we should be able to achieve that."