Well, EU was never dependent on Russian oil. Oil is a commodity. A large international market for it exists and it is cheap to transport, and sufficient import throughput was always possible. So there was no dependence: at no point Putin could say, "do X or else we will cut your oil supply" - that won't have any effect, they'd just buy oil elsewhere (heating market up considerably yes, but entire world market in which Russia doesn't have such a high share, equally). Russian choice would be to either sell it's oil to someone else instead, resulting in no effective change and no pressure applied to Europe at all, or not sell it to anyone and ruin his country, but having everyone else pay probably, double or triple the price to Arabs/USA for the oil they import.
What changed now is that he has to sell that oil to others at a steep discount leaving him almost no profit, with the middlemen making all that profit instead - which is OK.
But, EU statement mainly referred to gas, not oil. With gas, situation is a lot clearer - Russia simply stopped producing the gas EU stopped buying, because they can't technically sell it elsewhere, and EU buys it mainly from USA. It took almost a year for market to readjust but now the prices are same as they used to be before all these events.