The O's lost 5-0 at Accrington on Tuesday, six days before a winding-up petition is due to be heard.
"It was a very hurtful night - certainly my lowest night in football," Webb, 33, told BBC London.
"I'm trying to take on a lot, carry a lot of things on my shoulders. It's hard."
Newport's win at Morecambe on Tuesday saw Webb's side go bottom of the fourth tier for the first time this season.
Orient have lost five of their last six games and are seven points from safety with nine matches remaining.
Webb, who is in his first management job, added: "I'm trying to reassure players about winding-up orders, and reassure myself really because I haven't got a clue what's going on either.
"The whole thing's testing, but really all we should be worrying about is setting the team up to try and win a football game.
"Unfortunately, your heart sinks when it goes to 2-0 because then it really is game over when you're down the bottom."
Orient will present a "funding plan" at the High Court to stave off Monday's winding-up petition, according to the English Football League.
The club met with EFL officials and said they would be able to clear the debt, believed to be around £250,000, owed to HM Revenue and Customs.
"We were advised that a funding plan is in place to clear the petition debt and to complete their remaining nine league fixtures," an EFL statement said.
"We remain in regular dialogue with the club and, as the competition organiser, the EFL will continue to offer whatever practical assistance is available to us as the club continues to navigate itself away from their current position.
"The issue of the ownership of the club is not a matter for the EFL, as long as our regulations are met and any sale of the club is a matter for its shareholders, at this stage."
President Francesco Becchetti said last month he would consider selling Orient, but it is understood a number of potential offers have not been considered sufficiently financially attractive.
Leyton Orient manager Danny Webb says the club's off-field problems are weighing on him heavily after they slipped to the bottom of League Two.