Grigg is part of the 23-man Northern Ireland squad for the ongoing Euro 2016 finals, but he was an unused substitute against Poland in their opening Group C game at the Allianz Riviera in Nice on Sunday.
Poland won the match 1-0, thanks to Arkadiusz Milik’s goal in the 51st minute.
Paterson, who can play as a winger or as a forward, has claimed on Twitter that Grigg should have featured in the game.
The 24-year-old striker was in brilliant form for Wigan Athletic in League One this past season and helped them win promotion to the Championship.
Paterson played with Grigg at Walsall, and he believes that his former teammate should have played some part for Northern Ireland against Poland on Sunday.
I may be a bit biased but how @WillGrigg didn't get on the pitch— Jamie Paterson (@jamiepaterson12) June 12, 2016
Paterson has been on the books of Forest since 2013 and has a contract with the Reds until June 2018, according to Transfermarkt.co.uk.
The 24-year-old spent the 2015-16 campaign on loan at Championship rivals Huddersfield Town.
The attacker scored six goals and created 50 chances in 34 league matches for Huddersfield this past season.