Notts will face reigning Friends Provident Trophy champions Durham Dynamos at Riverside on Wednesday 4 June following their Duckworth-Lewis defeat to Leicestershire Foxes.
In a rain-affected game, the Outlaws fell 13 runs short, reaching 47-3 from 12 overs after Leicestershire posted 147-7 from 35.
"The rain didn't help and it was a difficult game to get in to but the important thing is that we have qualified," said Notts Director of Cricket Mick Newell.
"Our fielding was much improved and Graeme Swann and Samit Patel bowled very well for us.
"Durham won the competition last year and we know that they posted a good score against Derbyshire on Monday and they will be very strong."
Notts needed 26 from their final ten balls to win but their chase was disrupted when Mark Wagh was run out and Adam Voges stumped to give the Foxes the win they needed to win the group and secure a home quarter-final.
Friends Provident Trophy quarter-final draw (matches to be played Wednesday 4th June):
Durham v Nottinghamshire
Gloucestershire v Yorkshire
Kent v Somerset
Leicestershire v Essex