Lagrell announced that Eriksson, 61, had decided it was not possible to take on the job because of his commitments to the League Two club.
Eriksson had been one of a number of names linked with the post following the resignation of Lars Lagerback nine days ago, but has instead decided to honour his role as director of football at Meadow Lane.
"Last week we made contact with 'Svennis', who is one of the people we thought could be a possibility for the job as national team coach," Lagrell said in a statement.
"We have had good discussions but he has now decided that, with regards to his contract with Notts County, there is no possibility of him taking charge of the national team now.
"There's nothing dramatic about this, we simply had a chat to see how the land lies."
Lagrell admitted Eriksson had been top of their list to replace Lagerback, who stepped down after Sweden's failure to qualify for the World Cup finals.
He also hinted the former England boss had proposed combining the
Notts County and Sweden jobs, but his current employers would not allow it.
"We can state that in the race the leading candidate has been crossed off," Lagrell added: "Svennis rang me and said 'the (Notts County) owners have put a stop to my idea'.
"We hadn't promised him anything and he hadn't promised us anything. I was frank with Svennis when we spoke and said I would also be ringing a handful of other candidates.
"We never reached a stage where we were discussing eventual financial questions."
The SvFF revealed on Monday they have a shortlist of "five to 10 names" which also includes Fulham boss Roy Hodgson.
And Lagrell will now turn his attention to their other options as they look to plug the gap left by Lagerback's resignation.
"We'll now continue to talk to the other candidates the board have and we hope to be able to present a replacement as soon as possible," he said.