Hamburg side have started the new season slowly and have just a single point from their first three games of the campaign.
The heat is on Fink, but he is buoyed by what he has seen from his team in training this week and is sure they will deliver the goods against winless Braunschweig.
"I've felt a reaction from them," said Fink. "The lads want to show everybody that they still have aims.
"Giving up is not what we're good at, and that is a saying which applies to us well."
And Fink has the backing of his bosses, despite the poor start.
"We want continuity in this position and Thorsten Fink enjoys our faith," Hamburg chairman Carl-Edgar Jarchow told Kicker magazine.
"He knows that he will be viewed with a critical eye in his third year and he is dealing with that well. We're supporting him also."
Fink has also received support from Braunschweig defender Ermin Bicakcic, who says he is not reading anything into their early-season form.
"It doesn't really say much that they only have one point," he said on the club's website.
"What is important is that we prepare ourselves well. We've got to work as a team, but each individual has got to be mentally well-prepared too.
"We have shown what we are capable of against Bremen and (Borussia) Dortmund already (they lost the games 1-0 and 2-1 respectively). We must keep our heads up and carry on."
Braunschweig arrive in Hamburg with a full squad, while Fink is also expected to have a fully-fit squad to choose from, with Rafael van der Vaart set to be fit.
"I expect him to be able to play," said Fink of the Dutchman.