The Welsh region currently prop up Pool One after suffering three defeats from four starts, results that have left them four points behind Sunday's Liberty Stadium visitors Northampton and eight adrift of leaders Leinster.
The Ospreys meet Leinster in Dublin next Friday, and Tandy has not given up hope of featuring in the quarter-final mix, despite odds being stacked against it.
"Both teams need the win on Sunday, so it is going to be explosive and physical. I am sure it will be a great contest," he said.
"The results in the last round mean that there is a chink of daylight for us, and you can guarantee that we will be going for it.
"We know that to have any hope of progressing we have to do our bit, which means a win on Sunday is essential.
"We are improving week on week, but to get a result against a team of Northampton's stature then we will need to move up several levels."
Saints' defeat of Leinster last time out in Europe revived their European chances, although a loss on Sunday and an away success for Leinster against Castres would mean the Irish heavyweights will progress as group winners.
Aviva Premiership leaders Saracens, meanwhile, tackle Toulouse in France on Sunday with the teams locked on 15 points at Pool Three's summit.
Toulouse toppled Saracens by a point at Wembley in October, but the Premiership outfit have discovered irresistible form of late, highlighted through their 29-8 victory against Gloucester last weekend.
"If the game at Wembley taught us anything it is that we need to be switched on for the whole game," Saracens' England international full-back Alex Goode said.
"We dominated that match against a top side that are full of internationals, so this time it is a case of making sure we finish off the job.
"Our concentration has to be spot-on for the full 80 minutes, but if we don't go into our shells and we back ourselves, then there is no doubt in my mind that we can go there and win it."
Chris Wyles replaces centre Marcelo Bosch, who rests a slight knock, as Saracens' solitary change from the Gloucester game, while Toulouse parade their usual array of big-guns, including full-back Maxime Medard, flanker Thierry Dusautoir and number eight Louis Picamoles.