"Today, the coach offered his resignation which was accepted by the club," Tom said on their website.
Sunday's defeat was Tom's sixth in the last seven league games, leaving the in-debt club third from the bottom midway through the season.
Since being appointed Tom coach in 2008, Nepomniashchy had kept them in the top flight despite a permanent shortage of funds.
In 2009, Tom avoided going out of business because of mounting debt after the intervention of Prime Minister Vladimir Putin, who ordered seven of Russia's largest oil and energy companies to rescue them.
This year, the players threatened to go on strike after not being paid for several months as Tom again had to seek money from the government to keep them afloat.
In addition, the club and its general director Yuri Stepanov have been under criminal investigation for embezzlement, linked to the 2006 transfer of Russia striker Pavel Pogrebnyak.
Reports said a third party had been paid $400,000 to obtain Pogrebnyak's transfer from Spartak Moscow to Tom in 2006.
Pogrebnyak, who moved to Zenit St Petersburg in 2007 before joining Bundesliga club VfB Stuttgart two years later, and his agent, Oleg Artemov, have denied any wrongdoing.
Nepomniashchy has been mostly known for guiding Cameroon to the quarter-finals of the 1990 World Cup in Italy where they became the first African team to reach the last eight.
The much-travelled 68-year-old has also coached national teams and various clubs in Turkmenistan, Turkey, China, South Korea, Japan, Uzbekistan and Russia.
