mens rea : a culpable mental state especially : one involving intent or knowledge and forming an element of a criminal offense

It doesn’t. Otherwise one could just say “Sorry I was daydreaming and simply didn’t today attention.” and get off the liability. This is, in fact, the relevant word:

Many traffic offences, including speeding, are considered strict liability offences in virtually every jurisdiction, which means that it is sufficient to prove that the act occurred and it is unnecessary to prove intent. In such cases, whether or not an offender meant to commit the offence is irrelevant. For strict liability offences, lawyers are unable to argue that the offender had no knowledge or intentions of committing the offence because what counts is whether the offence was committed.

A judge would simply look if the elements are proven:

a) the offence was committed b) no lawful excuse or defence for doing so exists

However, there is the defence of reasonable mistake. This means that it is sometimes possible for strict liability traffic offences to be refuted if the offender can successfully argue and provide evidence to show that they were genuinely mistaken and did not know they were committing the offence. However, this is different from the mens rea principle.