Milan scored four times in the second half to prevail 5-2 on Thursday, but not before falling behind to their modest opposition.
Dominik Stolz and David Turpel silenced San Siro as they overturned Patrick Cutrone's 21st-minute opener with well-taken finishes either side of half-time.
The Rossoneri eventually recovered with two own goals and one apiece from Hakan Calhanoglu and Fabio Borini establishing a strong position ahead of their final Group F fixture away to Olympiacos, where a point or one-goal loss would be enough to advance.
"After the equaliser a bit of fear took over," Gattuso told Sky Sport Italia.
"We started well, but there are no easy matches. Dudelange kept trying to play and they were able to give us difficulties.
"But the important thing was to win. At 2-1 down the team reacted well and we pushed on the technical level and with character. I knew it would be hard to do."
The striker's influence waned after a bright beginning, which Gattuso attributed to a recurring injury.
"I think his back was bothering him," the Rossoneri boss said.
"He didn't say anything about it, I just had that feeling because he was having a hard time shooting. He's good at gritting his teeth and not giving in."