Kieran Richardson, of Northallerton Road, Brompton, North Yorkshire, made the threats on Twitter ahead of the game at Fratton Park on May 16.
His comments prompted the club to increase security measures.
Richardson was arrested on the day of the game and admitted making a malicious communication at a hearing at York Magistrates' Court in June.
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He was sentenced on Monday to a 12-month community order with a three-month curfew and 25-day community rehabilitation requirement, court staff said.
North Yorkshire Police said Richardson posted two tweets on May 15 in response to a message by a Portsmouth fan about an incident in which a smoke bomb was hurled at at Sunderland supporters during the clubs’ league clash on Wearside in April.
He wrote: "I wonder how many Portsmouth fans I can shoot. Everyone remember the Manchester Arena bombing, just imagine Fratton Park going bang.
"Well, let's find out tomorrow. PS I'm hoping to kill at least 150 Portsmouth fans, fingers crossed."
In another tweet, he wrote: "Bomb, bomb Fratton Park, the Portsmouth fans will die. Going to be fun tomorrow."
Portsmouth and Hampshire Police made statements reassuring fans that increased policing and security would be in place at the match.
The play-off second leg passed off peacefully with the 0-0 draw ensuring Sunderland reached the League One final with a 1-0 aggregate win.
Court staff said Richardson was ordered to pay an £85 surcharge and £85 costs.