First, concave utility function is just a model for risk aversion which is "the reluctance of a person to accept a bargain with an uncertain payoff rather than another bargain with a more certain, but possibly lower, expected payoff." (wiki)

Second, the certainty effect is indeed one of the effects that is captured by my preferred model, but of course it's not limited to it, because it's possible to behave in a risk-averse manner even if none of the offered bets are certain.