As far as I know tsunamis are caused by landslides at the bottom of the sea. But an asteroid impacting the sea is a different phenomena. Could it still cause a "tsunami" as in an unstoppable mass of water propagating towards the shores? Is there a need of distinction between these two phenomena, or do they add up to the same thing?
An asteroid impact in the ocean is an oversized example of throwing a pebble in a pond - both will produce waves in a concentric pattern from the point of impact.
The height of the waves and the energy they would have would depend on the amount of energy the asteroid transferred to the water at the impact sight.
The energy transferred will depend on the kinetic energy of the asteroid at the moment of impact, this being a function of the mass and velocity of the asteroid; based on the classical equation for kinetic energy: $E_k = 0.5mv^2$.
Hence, an asteroid with a very large mass and high velocity could transfer enough energy that could create tsunamis. The best example of this is the impact that created the Chicxulub crater in the Yucatan peninsular, that lead to the creation of the K-T boundary and the extinction of the dinosaurs.
That impact created a mega tsunami that affected the coastal southern state of the USA, from Texas to Florida.