Hans Backe left his job as manager at the club on Tuesday after just seven weeks and nine games in charge.
“I am aware that Hans’ decision has led to speculation about my own position here at Notts County,” said Eriksson.
“I continue to enjoy my work at Notts County and together with [new owner] Peter Trembling I hope to progress to the goals that we have set.”
He added: “Everyone at the club is disappointed that Hans has chosen to tender his resignation.
“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.
“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.”