The Rams were knocked out of the FA Cup by Blackburn last week but responded with a ruthless Championship display in front of their home fans as goals from Craig Bryson, Jamie Ward and Andy Keogh sunk the Terriers.
"It was a disappointing performance last week so we wanted a response and we got one today," Garner said afterwards.
"We were outstanding from the first minute to the last and everybody was on top of their game out there. There's no reason why we can't make the top six.
"It's a very good squad in terms of effort and honesty and when we are on it, we are as good as anything in this division.
"We scored three excellent goals and it was a magnificent finish from Jamie Ward. He's getting back to full fitness, three weeks ago he couldn't even lift his leg that high.
"It was a very good all-round performance from him because he also brought other players into the game."