Aged 15 years and 300 days, Ødegaard came on as a second half substitute after 64 minutes in the 2-1 win over Bulgaria.
"I was a bag of nerves when I came on, but with the welcome I got from the crowd I just had to smile and get on with it," he told the Verdens Gang newspaper.
"I think it went well and we came away with three points - that's the most important thing."
Ødegaard plays his club football in midfield for Strømsgodset in the Norwegian top flight, but is attracting interest from some of the top clubs in Europe. Barcelona, Liverpool, Manchester United and Real Madrid are all said to be keen to sign the teenager.
Previously the youngest player to turn out in a Euro qualifier was Sigurdur Jonssson of Iceland who was 16 years and 251 days when he represented his
country at that level.
The cap against Bulgaria was not the first for Ødegaard. He played against the United Arab Emirates in a friendly in Stavanger on August 27.