Gary Holt was less than pleased with the manner of Livingston's 2-1 victory but admitted he was delighted to avoid the "ridicule" of a Betfred Cup upset against Forfar.
The Lions manager knew his team's trip to face League One opponents was being eyed by some for the possibility of a shock in the last 16 of the tournament.
However, the Premiership side avoided any slip-ups, thanks to goals either side of half-time from Lyndon Dykes and Scott Pittman.
Dykes lost his marker to bullet in a header from a Steven Lawless corner and Pittman drilled low past Forfar keeper Marc McCallum following excellent work from Robbie Crawford.
Dykes should have added a third from close range before an error from skipper Alan Lithgow allowed Dale Hilson to run in on goal and pull one back with 28 minutes still remaining.
But the part-timers could not muster any clear opportunities as Livingston held on to book their quarter-final spot.
Holt said: "We spoke about it before the game and we spoke about it during the week, it's one where we could be on the end of the giant-killing.
"We could be picking up the papers on Sunday morning and we're getting ridiculed because we've been beaten by a lower-league team.
"So, we knew we had to come here and we had to battle.
"The conditions meant it was never going to be pretty, when the wind was blowing and swirling, but I'm pleased we're through."