You were OK to cross the runway without stopping, but it is also OK to ask
the controller if the coast is clear. Barring that, if there is more than
one pilot on board, it is good practice for each pilot to look to his side
and announce "clear left" or "clear right" before crossing either a runway
or a taxiway.

Many pilots and controllers would like to see the rules changed but the
downside is that requiring each aircraft to call the tower or announce on
CTAF before crossing every runway can increase the radio chatter
considerably. There are pilots here that go ballistic just because some
people use a couple extra words such as "with you." They are likely to be
intolerant of the increased radio traffic that would be generated by a
change of the rules for taxiing.