The Bairns are being forced to make cutbacks after losing their Clydesdale Bank Premier League status.
Moutinho scored five goals after rejoining the club for a second spell last November, while fellow forward Showunmi netted just once since arriving in January from Leeds.
Moutinho said in the Daily Record: "I am happy and settled and my family love it here. I don't know what the future holds but I would definitely prefer to stay in Scotland."
Showunmi was informed of his departure following a meeting with manager Steven Pressley on Wednesday.
He said: "I've spoken to Pressley and I won't be at Falkirk next season.
"He just said I wasn't to be offered a contract and thanked me for my efforts in trying to keep the club up.
"A lot of people didn't think we would even take it to the last day and it's unfortunate we couldn't score the goal we needed.
"The team had to put up with a lot of knocks and I'm sad we couldn't do it. I'm a free agent now and must see what options are on the table. I've enjoyed my time up here and if the opportunity arose to stay in Scotland, I'd consider it."
Source: PA
Source: PA