Dortmund had 20 shots against the league's bottom side but were denied on numerous occasions by Braunschweig keeper Daniel Davari, before finally sealing the victory courtesy of a Pierre Aubameyang brace.
Klopp concedes that his side were not at their best for the match, but is keen to move on as they look to close the gap on second-placed Bayer Leverkusen in the Bundesliga table.
"We had a load of goalscoring opportunities, but Davari pulled off some unbelievable saves," Klopp is quoted as saying by the Bundesliga's official website.
"We haven't had many scrappy victories this season, but this one certainly was. If you're not completely focused, you have to fight for the win. Now we move on."
Dortmund face 12th-placed Werder Bremen next Saturday as they aim to win back-to-back league matches for the first time since October/November.