Think of how many level of people are there.
There are the guys that shot the missile. The ones that command those guys, the ones that command those and commanders above those.
In the chaos of the tragedy, no body wants to open their mouth, in case they are executed for saying something that is against the direction which the nations top leaders want to take.
Then come the top leaders. With the escalating tensions with the US, having recently sent a barrage of missiles to Iraq, they are holding on to the horses of the country, on the edge of a cliff.
They have to discuss and deliberate a myriad of issues that are consequential to their every word.
They cannot be too rushed to say that they shot the plane down. It might create a chance for the US to spin this as a deliberate murder.
And all these are humans. Humans that run nations, whose millions of peoples lives are at stake.
Three days is perfectly OK.
I am glad Iran is honest enough to admit it's mistake, unlike Russia, for example.