Schalke coach Fred Rutten admitted he had been nervous ahead of his side's 3-0 DFB Pokal win over Homburg - his first game in charge of the club.
The Royal Blues advanced comfortably to the second round of the competition on Saturday, along with 10 other Bundesliga outfits.
And former FC Twente boss Rutten was relieved his side did not fall victim to a giant-killing.
"Such games against lower-league opposition are always very difficult and sometimes things can happen that you do not expect, but we are through to the next round and that is the most important thing," he said.
Another coach starting his first season at a new club, Dortmund's Jurgen Klopp, felt there was room for improvement after his team beat Essen 3-1.
"Not everything was perfect, but the team showed the new face that we have been talking about for five weeks," said Klopp.
Bochum survived the biggest scare of the Bundesliga sides as they needed a penalty shoot-out to edge past Munster.
"That is the rule of the cup - when you don't score early enough, then the opponent excels themselves and makes life particularly hard for you," coach Marcel Koller said.
"We had enough chances, but our former goalkeeper David Buchholz had an excellent day."
Seven further Bundesliga sides start their cup campaign on Sunday.
