The home side could not find a way past inspired Orient goalkeeper Jamie Jones, who produced a string of fine saves to deny Jack King twice and Nicky Wroe late on.
Orient rarely threatened and as a result saw their three-match winning run come to an end to lose ground in their push for a play-off place. They currently sit ninth, three points behind Yeovil in sixth.
"We're happy to get a point after not being at out best really, but we dug the result out in difficult conditions," Nugent said.
"Nathan Clarke and Jamie Jones were excellent, if it wasn't for them we would've gone in a few goals down at half-time.
"Nathan Clarke was spot-on, immaculate with his whole performance.
"The injury break is difficult, but it's the same for both players, certainly it didn't help, but there's not an awful lot we can do about that.
"You want to win every game, but you can't and we didn't want to lose.
"Early in the season we possibly lost or drew games where we played really well but here we got a point from not our best performance.
"Where we are relative to the top six is irrelevant really, we have to go and win the games, all you can do is look after yourself and see where it takes you."