Backe spent only seven weeks as County’s manager after being appointed by fellow Swede Eriksson on a three-year contract in succession to Ian McParland.
Backe told the squad he was leaving ahead of training here on Tuesday and his exit immediately sparked speculation about Eriksson’s position with County.
However, in a statement on the club’s official website, nottscountyfc.co.uk, Eriksson reiterated he was not leaving Meadow Lane.
“Everyone at the club is disappointed that Hans has chosen to tender his resignation,” said Eriksson.
“This has come as a surprise to all of us in the context of recent results on the pitch and the completion of the management buy-out of the football club by Peter Trembling.
“I am aware that Hans’s decision has led to speculation about my own position here at Notts County.
“I wish to make it clear that I believe the management buy-out is a positive first step for the club and we look forward to confirming further investments for the future.
“I continue to enjoy my work at Notts County and, together with Peter Trembling, I hope to progress to the goals that we have set.”
Last week County chairman Trembling completed a takeover from Middle East owners Munto Finance, only five months after the latter took control with an ambitious bid to turn the club into a top-flight side within five years.
Backe was in the dugout for just nine matches, his final game in charge being Saturday’s 2-1 home defeat by Accrington Stanley – a result that left Midlands side County in sixth place and still challenging for a playoff place but 10 points behind leaders Rochdale.
Trembling said he was disappointed Backe had not stuck with the club while he talked to new investors, telling Sky Sports: “Sven and I are working round the clock on that and, come the middle of January, we could be in an extremely healthy position and not only back on track but maybe further down the line from where we expected to be, so I am disappointed that Hans has not waited around for that to happen.”
Assistant manager Dave Kevan will take charge for next week’s trip to Bournemouth.
Munto promised to invest millions of pounds when the consortium took over the club but former Arsenal and England defender Sol Campbell was the only high-profile arrival and he walked out after just one match.
County also had to deal with a winding-up petition issued by the High Court in November in relation to a six-figure debt accrued before Munto took over.