But after cruising past Glasgow Warriors in Round One, the former Australia ace has revealed the Cote d'Azur club's desperation to do the double.
"We've got a taste for it now," said Giteau.
"The feelings we went through last year when we won it were incredible.
"We spoke about wanting to get back there to do it again and prove we are a quality side that can not just perform for one year but year in, year out.
"With the support we get and the how much rugby means to this region we know the level of expectation upon us and the need for us to perform.
"But it's not just for the crowd, with the level of player we have here, it is for ourselves as well."
Jonny Wilkinson agrees with Giteau and is confident Toulon can do the double but he insists they must put together performances for the full 80 minutes.
"The answer is easy. Not because we're arrogant, but it's just a matter of attitude: we believe can win every game we play," added Wilkinson.
"But we need to be more professional and have a better connection throughout the team
"We have to keep the good habits to attack but it must be done for 80 minutes, 50 or 60 is not good enough."
Giteau started the encounter in the centre but switched to fly-half and pulled the strings superbly following a hand injury to Wilkinson.
But with a star-studded squad at Stade Felix Mayol, Giteau is just pleased to be on the pitch, regardless of what number is on his back.
"With the quality of players we have, the number of internationals we have, I'm just happy to play anywhere.
"You often hear that from players and it is a cliché but for me it's true. I'm enjoying my rugby at Toulon and with the talent of players we have here it's a really good atmosphere."
Toulon continue the defence of their Heineken Cup crown in Pool Two, against Cardiff Blues on Saturday.