The Arsenal captain had already released the ball when Silva closed him down in stoppage time and caught him around the Achilles and ankle area.
Odegaard went down in pain and needed treatment before continuing for the final minutes of the match. Silva was shown a yellow card for the challenge.
After the game, Odegaard made it clear he was unhappy with the incident.
"It has no place on a football pitch. It's embarrassing that people do things like that," Odegaard told TV 2.
"He loses his head. He just kicks me long after I've played the ball. I don't understand what he's doing."
The Norway captain was also asked whether Silva's connection with Premier League rivals Manchester City had any bearing on the challenge.
"You'd have to ask him about that. I don't know what he's up to," Odegaard said.
"That kind of thing doesn't belong on a football pitch. It's embarrassing that people do things like that. But that's life."
Odegaard also indicated that Silva had not apologised after the incident.
Silva was later asked about Odegaard's comments but did not offer an explanation for the challenge.
"It's football, my friend," he replied, according to Dagbladet.
Odegaard was seen limping as he left the stadium, leaving some concern over the Arsenal midfielder's condition.
Portugal's victory ended Norway's unbeaten home run at Ullevaal, with their previous defeat there coming in October 2023.
Portugal next face Denmark, while Norway take on Wales on Thursday.