No, a 'Critical' effect is not the same as a Natural 20
This is backed up by This Answer which helps differentiate between rolling a 20 on a d20 and landing a Critical.
Take the Sword of Sharpness or Vorpal weapons, for instance. For these magical weapons to activate you must roll a 20 on a d20 , which is not the same as landing a critical hit. This is farther proven when you include the Fighter's Improved Critical ability which allows them to land a Critical on a roll of 18, 19, or 20. In this case if a fighter landed a Critical with a roll of 18 with a Sword of Sharpness, all of the rules for a critical hit would apply; only the extra slashing damage would NOT apply as the fighter did not, in fact, roll a 20; he only rolled an 18.
Sentinel at Death's Door would only save you from effects that happen as a result of a critical hit; such as the Brutal Critical Barbarian feature or the extra dice included normally in a critical hit; not effects the require a natural 20. The wording here matters for certain features, abilities, and magical effects.
Keep in mind that attack rolls (spell or weapon attacks) automatically crit on a roll of 20; but dispite the connection this is NOT the same as a feature, ability, or magical effect that requires a flat 20 to be rolled as proven above when criticals are possible without rolling a 20.