The Whites were 3-1 and 4-2 up against the Northern Premier League outfit at Crabble but ten-man Marine fought back and made it 4-3 before a tense last five minutes.
Kinnear’s side may not have hit the heights they have at times this season but the boss was relieved to make it into the last 16.
“It wasn’t a great performance but you’ve just got to get through to the next round,” Kinnear told the club’s YouTube channel.
“The players are disappointed because they want to play well but you can’t play really well in every game.
“Marine didn’t lie down when we went two goals ahead twice. Cup competitions in this country are great and we’re just happy to be still in it because a lot of teams in our division aren’t.”
Dover face a difficult trip to play-off rivals Boreham Wood next Saturday, a club they have struggled against in recent times.
“When I came back here, people were saying that they were a bogey team for us,” Kinnear added.
“They’re a very good side, well organised and have invested in their team. It’ll be difficult but we’ve gone and got results in big games before.”
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