Soon after his arrival at the Capulet tomb with the discovery of the tragedy, Prince Escalus, on having listened to Friar Laurence's testimony, addresses the Capulets and Montagues expressing his disappointment. During his speech, he says the following:
"And I for winking at your discords too
Have lost a brace of kinsmen: all are punish'd."
It is not so much that the Prince blames himself for the tragedy, but he does take responsibility for not having done enough to stop the feud between the families. He says that he was only "winking" at their strife. This suggests that he feels that he had temporarily closed his eyes to their battle, choosing to, at most, ignore the ongoing dispute. The Prince essentially puts forward that he could have done more and that, if he had done so, the present tragedy would not have occurred.
He furthermore proposes that, because of his reasonably dismissive attitude, he had also suffered loss. Two of his kinsmen (Mercutio and Paris) have died. A firmer and much more hard-handed approach to end the quarrel between the two warring factions, might have prevented this unnecessary tragedy.
One can sympathize with the Prince, for on the whole, he had intervened and had promised both families severe sanctions if they should indulge their whims and strike out at each other. At the beginning of the play (Act 1 scene 1) he had warned both families:
"If ever you disturb our streets again,
Your lives shall pay the forfeit of the peace."
And again, after both Tybalt and Mercutio were killed in battle, he banished Romeo and warned:
"But I'll amerce you with so strong a fine
That you shall all repent the loss of mine" and
"I will be deaf to pleading and excuses;
Nor tears nor prayers shall purchase out abuses:
Therefore use none: let Romeo hence in haste,
Else, when he's found, that hour is his last."
He had clearly taken a tough stance, all to no avail.