"Everyone at Toulouse, and at other French clubs, has come to realise that the Heineken Cup is the biggest competition there is," he said. "We have made a successful defence of our European title the top priority at the club this season, putting the Heineken Cup ahead of the French Championship.
"We caught a cold in Edinburgh in the first round when we lost at Meadowbank and ever since that defeat we've been targeting the return game. We're hoping for a full house of almost 20,000 at Stade Ernest Wallon on Saturday - it's going to be a huge game.
"Edinburgh have improved dramatically this season and are the only unbeaten team in the tournament going into the last round. They are also the only team to be guaranteed a place in the last eight at the moment."
However, there was some tough talking in the Toulouse dressing room at half-time at Headingley Stadium yesterday (Sunday) as the reigning champions found themselves locked at 3-3 with Leeds Tykes.
"The coaches laid it on the line and told us we had 40 minutes to save our season," said Brennan. "A defeat would have virtually put us out of the Heineken Cup and we knew we had to get our act together.
"We would have been happy to have just come away with a win, but to pick up a bonus point as well was a fantastic turnaround. It means we can go into the game with Edinburgh with everything to play for.
"French sides are notoriously bad travellers and it was definitely a case of that in the first half at Leeds. All French teams like a bit of comfort and that comes with playing at home."
Edinburgh Rugby, the only team in the tournament still able to boast a 100 per cent record, head the group two points clear of the champions courtesy of their 23-16 home win back in Round 1 in December, with coach Frank Hadden adamant "we will be pulling out all the stops on Sunday.
"We are absolutely delighted to have qualified but everyone knows how hard it is to win the Heineken Cup without home advantage in the quarters.
"It will be incredibly tough as Toulouse is one of the hardest places to go and win - they are significantly better than a number of international sides - but, while we used to go there worried about the outcome, now we are confident we can compete against them on their home ground.
"We now know each other pretty well after also playing them twice last season and I think they have made progress since we played them in December.
"But essentially they are the same side with the same players who play an attractive game that does carry a certain risk element. We are looking forward to what is certainly a massive challenge."