Eriksson receives an ovation from the fans
The Magpies' new director of football received a rapturous reception from home fans when he walked out on the pitch before kick-off.
He watched his first game from the directors' box in the Derek Pavis Stand.
New strikers Luke Rodgers and Lee Hughes made themselves instant heroes with the County fans with second-half goals, while Lewis McGugan netted for the Reds.
The game was delayed by almost 15 minutes as supporters still poured into the stadium at 3pm.
In front of a bumper crowd, the opening stages were frantic and full blooded but neither side created any chances to break the deadlock.
McGugan launched a threatening attack on 16 minutes, intercepting a pass from Mike Edwards just inside the County half.
He quickly gave the ball to Robert Earnshaw and continued his run into the penalty area, but the Wales striker's return pass was too strong and went out harmlessly for a goal-kick.
Notts gifted the visitors another chance minutes later when captain John Thompson dawdled on the ball and was dispossessed by Dele Adebola.
The big striker held him off as he broke into the box and drove a low cross along the six-yard box that just eluded Earnshaw.
It was Forest's new Polish midfielder Radoslaw Majewski who had the first shot of the game on 26 minutes, testing Russell Hoult with a rising effort from just outside the box.
Hoult then pulled off a good save to deny Earnshaw from close range a minute later and held a header from Adebola low down to his left, as Forest began to put the Magpies under pressure.
But he made a mistake just after the half-hour mark, with a poor clearance straight to McGugan, who failed to capitalise on the chance and blazed over the bar.
Earnshaw then miscued badly wide from the edge of the penalty area, with time and space for better, and then flashed an effort across the face of goal and narrowly wide of the far post.
It was the closest they came to taking the lead in the first half.
Notts introduced Rodgers for Sean Canham at the start of the second half and he made an immediate impact, hitting the post with a low shot from inside the box.
Kevin Pilkington came on for Hoult and Luke Chambers replaced Kelvin Wilson, who limped off at the end of the first half, for Forest.
Pilkington was called into early action, saving from Adebola from close range.
Rodgers fired County ahead on 56 minutes, capitalising on a slip by Chambers to drive the ball past Lee Camp from inside the penalty area. It was a clinical finish from the striker, his sixth goal of pre-season.
Hughes doubled their lead on the hour mark, placing a close-range header past Camp at the far post from Craig Westcarr's right-wing cross.
Hughes was then replaced by Delroy Facey.
Forest made four changes on 66 minutes, changing their strike-force completely, with Dexter Blackstock and David McGoldrick replacing Earnshaw and Adebola.
And they reduced their arrears on 74 minutes when McGugan hit a shot from fully 25 yards, maybe more, that caught Pilkington out. The Magpies' substitute stopper got a hand to it but only palmed it into his own net.
Blackstock than dragged an effort wide of the far post as the visitors sought an equaliser.
Notts played much better in the second half and took their chances brilliantly – Eriksson must have been pleased.
NOTTS: Hoult, Moloney, Edwards, Lee, Clapham, Westcarr, Bishop, Thompson, Davies, Canham, Hughes. Subs: Pilkington (for Hoult, 45), Fairclough (for Westcarr, 82), Hunt, Rodgers (for Canham, 45), Mas, Facey (for Hughes, 62).
FOREST: Camp, Wilson, Lynch, Morgan, McGugan, Adebola, Earnshaw, Tyson, Majewski, Gunter, McKenna. Subs: Chambers (for Wilson, 45), Mitchell (for Chambers, 66), Blackstock (for Earnshaw, 66), McGoldrick (for Adebola, 66), Darlow, Davies (for Tyson, 79), Anderson (for Majewski, 66).
ATTENDANCE: 12,040 (5,885 away).