What concerns Claudius most about the murder of Polonius is his realisation that he could very easily have been killed if it were him hiding behind the arras rather than Polonius. He says as much in response to the news:
It had been so with us had we been there.
He also goes on to express his regret that he let Hamlet continue to enjoy freedom when it was clear that he was plotting some kind of violence. As king, he recognises that he should have paid attention to the signs earlier and done something to restrict his freedom so as to protect himself and his people. What is interesting about this scene however is that Claudius now clearly suspects that Hamlet knows what he did to his father and how precisely his father died. He therefore acknowledges that Hamlet's actions are not the result of any madness, but a deliberate, cold plot to kill him. He however is not able to reveal this to Gertrude, and so has to watch his words very carefully. The murder of Polonius however certainly increases the tension, as it shows just how far Hamlet is willing to go in order to bring about his revenge. Claudius begins to fear for his own person.