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.

Multiple attacks in the French capital on Friday killed 129 people.
The 2024 Olympic hosts will be named in 2017 and Bach said: "IOC members know terrorism is not a French or a Parisian problem, it is a global challenge."
On Sunday, Euro 2016 organiser Jacques Lambert said next year's tournament in France should not be cancelled.
Rome, Hamburg, Budapest and Los Angeles are also bidding for the 2024 Games.
Asked whether Friday's attacks could influence the vote, Bach told French sports daily L'Equipe: "No, the IOC members have a lot of experience.
"We are talking about the Olympic Games that will be held in nine years and terrorism is global, it is not just about a country or a city.
"It does not only concern sports but all the big events and the whole society."
He added: "You cannot concede victory to the terrorists.
"We must be united and firm, especially with the Olympic Games."
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.
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Last week's attacks on Paris will not influence the city's chances of hosting the 2024 Olympic Games, IOC president Thomas Bach has said.