Strictly speaking, Critical Failures don't exist in 5E
There are three kinds of d20 rolls: attack rolls, ability checks, and saving throws. However, ability checks and saving throws do not automatically fail on a natural 1. The times when natural 1's have a significant effect are called out explicitly for some rolls, but not for all rolls in general.
Nat 1's auto-fail for attack rolls
Rolling a 1 or 20, PHB pg 194
[...] If the d20 roll for an attack is a 1, the attack misses regardless of any modifiers or the target's AC.
Nat 1's have a crit fail-like effect on death saves
Meanwhile, death saving throws are a special case of saving throw in which it is possible to fail in a much more severe way when you roll a 1, as opposed to another low roll that would simply fail it.
Death Saving Throws, PHB pg 197
Rolling 1 or 20. When you make a death saving throw and roll a 1 on the d20, it counts as two failures. [...]
The PHB never says "critical failure" for anything, but it explicitly calls out effects that happen on natural 1's for attack rolls and death saves. Meanwhile, ability checks and general saving throws do not get this same treatment. This means they do not auto-fail or crit-fail on natural 1's.
Variant Rule in the DMG
The DMG calls out that you may implement critical failure or success on ability checks or saving throws. This reinforces that critical fails or successes do not exist out of the box, but you are given text in RAW to support their implementation.
Critical Success or Failure, DMG pg 242
Rolling a 20 or a 1 on an ability check or a saving throw doesn't normally have any special effect. However, you can choose to take such an exceptional roll into account when adjudicating the outcome. It's up to you to determine how this manifests in the game. An easy approach is to increase the impact of the success or failure. [...]