Erik Botheim and Ola Solbakken scored twice each for the home side, who led 2-1 at halftime and ran rampant in the second period to stun the Italians.
It was the first time in 1,008 games as a coach that a Mourinho side conceded six goals or more.
He did rest a number of first-team regulars, perhaps in anticipation of a comfortable night, and was made to pay.
“I decided to play with this line-up, so the responsibility is mine,” the 58-year-old Portuguese told Sky Sport Italia. “I did it with good intentions, to give an opportunity to those who work hard and to rotate the squad on a synthetic pitch in cold weather.
“I never disguised the fact we were a squad with real limitations. We have 13 players who represent one team, the others are on a different level. We lost against a team that showed more quality on the night. It’s that simple.”
The defeat may not have been quite as painful for Mourinho as Real Madrid’s humiliating 5-0 loss to Barcelona in 2010 but Roma, who started the Europa Conference League with two wins, are now in second in the group on six points, one behind Bodo/Glimt.
Register for free to continue reading
Registration is a free and easy way to support our truly independent journalism
By registering, you will also enjoy limited access to Premium articles, exclusive newsletters, commenting, and virtual events with our leading journalists
Already have an account? sign in
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies