The Blues overcame near blizzard conditions in France to defeat Grenoble 28-3 and progress through to the knock-out stages in Europe.
They will travel to fellow GUINNESS PRO12 side Newport Gwent Dragons in the quarter-finals in April after the Dragons beat Stade Francais 30-19.
For the Blues, it meant back-to-back victories following their 104-12 win over Rovigo and sets them up nicely for their visit to Wasps on Sunday.
And while currently down in ninth in the GUINNESS PRO12 table, Hammett called for his players to rise to the challenge of the games ahead as the season starts to approach the business end.
"We have seen now for a couple of weeks that standards are in place and are concrete. That is always a challenge because the next time you go out that doesn't just happen," Hammett told Cardiff Blues' official website.
"We talked about that and how we are moving on to a new phase and that people are now into different challenges; internationals and LVs. It's now about maintaining standards and watching them grow.
"But all these challenges we have faced will make us stronger and help us grow and when we come back to this competition in a month, hopefully we will be in an even better position.
"We can be confident in areas of our game against any opposition but we know it's going to be tough in the quarter-final and we will probably go in as under-dogs. But that is an exciting challenge."
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