Head coach Toby Radford says Glamorgan have to "dig in and show fight" if they are to have a chance of maintaining their unbeaten Championship record.
Glamorgan were all out for 162 in their first innings on a weather-hit day, thanks to New Zealand all-rounder Jesse Ryder claiming a career-best 6-47.
"Ryder bowled exceptionally well," Radford told BBC Wales Sport.
"There were one or two false shots and a couple of decisions which could have gone the other way."
Essex were 78-0 at the halfway stage of the match, a lead of 195 runs.
Ryder took the first five wickets to fall with his medium pace and veteran paceman David Masters chipped in with three.
Glamorgan were unable to reproduce the lower-order recovery they have benefitted from so often this season, Colin Ingram top-scoring with 43.
It was Glamorgan's lowest completed first innings of the season, with 278 the previous worst.
"We look at the top six to get the bulk of the runs, the middle and lower order have done it all season, unfortunately we didn't quite do it today and it gave them a substantial lead," said Radford.
He is hoping that Glamorgan can produce a more spirited performance in the second half of the game, whether or not they get any help from the weather.
"When we do get to bat again we've got to just dig in, we've shown lots of fight all season and we don't give up on any cause," Radford added.
"There's certainly no doom and gloom with us, we're going to come positive and see where this game takes us.
"There's been a lot of showers, it's been murky and gloomy and there could be more around in the next couple of days. But I don't want the weather to save us, I want good-quality cricket to save us."
The Welsh county have so far won four and drawn five of their Championship games this season.