Palace had expected to enjoy a Europa League campaign having won the FA Cup in May, but they were demoted for breaching multi-club ownership rules.
That did not dampen spirits for their first Conference League fixture, though, and persistence brought about a hard-earned Palace win at Selhurst Park.
They continually pushed to find ways through the Norwegian side's defence, stretching them wide when possible in an attempt to open up gaps, and Mateta made the breakthrough soon after half-time.
All the same, Fredrikstad will be left with a glimmer of hope that they can overturn their deficit in the second leg.
With Eze absent, Palace were missing a creative edge.
They had 74.3% of possession and 25 attempts to score, but they hit the target with just five of those and only scored once despite their chances amounting to 2.31 expected goals.
While Fredrikstad were particularly solid in the early stages, they quickly tired and Palace did not make the most of that.
Fredrikstad are a side who are eighth in the Norwegian top flight. While they brought a fighting spirit to the match, Palace are far superior on paper, having recently beaten Liverpool to win the Community Shield.
Yet, without a clearer cutting edge in Norway next week, the Londoners risk letting this tie slip from their grasp.