Running and walking shoes, but especially running shoes - you really have to get ones that suite your feet. There are models that are best for people who, over-pronate (feet rolling inwards) over supinate (feet rolling outwards) or those who's are Neutral. I have one foot that over-pronates and one that over-supinates, both only mildy so. To combat this I purchased a pair of custom made orthotic insoles and put them in to a Neutral shoe.
Sometimes I take these out especially if doing high mileage 40 mile+, and replace them with a pair of Sorbothane Double Strike cushioned insoles.
Whatever make sure the shoes are well cushioned.
If you felt that both your feet were being pushed out, your feet are either neutral or over-supinating and the shoes were meant for an over-pronator, or the shoes were neutral and your feet are over-supinating.
Over-pronator shoes have built in compensating features together with more of an arch support, which lifts the arch or inside of your foot.
Neutral shoes have a more of a flat foot bed.
If using a custom made orthotic insole, it is best to put them into a Neutral shoe.
Of course it also be down to the fact that the socks you were wearing are particularly slippery on a medium arch support insole, causing your feet to slide outwards (I have experienced this)