It may have taken well over 210 minutes of football, but ultimately Palace prevailed against a Larnaca side who had only conceded once in the competition before the tie.
Ismaïla Sarr scored his fourth and fifth European goals of the season to secure a place in the last eight.
Hughes, who brought stability to the midfield after coming on as a substitute, admitted it wasn't Palace's prettiest win of the season.
But with last season's FA Cup triumph still fresh in memory, he knows the only requirement in cup competitions is progressing to the next round.
"We did it the hard way, as usual," he said after the win. "But ultimately, getting through was the most important thing.
"I bet it was entertaining much for a lot of the neutral fans, but I think our quality shone through in the end.
"It could have been a lot easier on the night, but again, we got through.
"We would prefer it not to be like that, but like I keep mentioning, ultimately getting through is the most important thing. They're not an easy team to play against. Look at their league record in the Conference League – they'd conceded just one goal, in the 93rd minute.
"I think that says it all about how well-oiled they are as a defensive unit. We had to be patient and we got there in the end."