Howard Saint is trying to punish the person who organized the police ambush.
During the arms deal, the police showed up and surrounded the participants (Bobby Saint, Mickey Dukas, and Otto Krieg). Immediately, Otto Krieg claimed that there was a snitch and blamed Bobby Saint:
Otto Krieg: You brought a cop, and he brought his fucking friends!
Of course, Bobby Saint did not actually bring the cops, but it does suggest that there is some suspicion of foul play involved, and that Otto Krieg felt the need to vocalize this suspicion...
probably because "Otto Krieg" was the one who brought the cops in the first place.
Howard Saint probably want to follow up on that suspicion, by investigating Otto Krieg's network and finding out any possible leads/"police snitches" that could have been responsible for setting up this police ambush.
While Howard Saint believed that Otto Krieg had died during the shootout, his death doesn't actually bring him any sort of satisfaction or feeling of vengeance/justice. After all, it seems reasonable to conclude that any plan that Otto had didn't involve Otto getting murdered by the police. The guilty party who caused Bobby's death by calling the police must be the party that gets punished, not some "innocent" bystander that may have helped organize the arms deal that led to Bobby's death.
Mickey Dukas: His name is Otto Krieg. And if it's any comfort to Mr. Saint, he's dead too.
Howard Saint: Well, it's not. It's actually no comfort at all.
As for why Howard Saint choose to target the person who organized the police ambush instead of, say, the actual police, it appears that Howard has a unique view of responsibility, as can be seen during the scene where Mickey Dukas was interrogated.
Howard Saint knew that Mickey Dukas had brought Bobby Saint along to the arms deal, thereby making it possible for Bobby Saint to get shot during the police ambush. Howard Saint allowed his thugs to beat up Mickey Dukas, and then later held Mickey up at gunpoint. But Howard didn't shoot Mickey. Instead...
Howard Saint: The man who is responsible for my son's death must die.
Howard Saint shoots Bobby's guardian
Howard Saint: I told you to never let him out of your sight.
In Howard's mind, the guardian should have prevented Bobby's death by preventing Bobby from following Mickey to the arms deal. But Mickey himself appeared to be innocent...he may have played a role in Bobby's death, but he didn't serve as the proximate cause of Bobby's death. If the guardian did his duty in stopping Bobby from following Mickey, Bobby would still live. Mickey wasn't responsible for what happened next.
If Howard Saint continues to follow this thought process, then Howard would never blame the police for killing Bobby. The police may have played a role in Bobby Saint's death, but they did not pull the trigger intentionally (so they should not get blamed). The only person who bear full responsibility is is the person who organized the police ambush in the first place, thereby serving as the proximate cause of Bobby's death. Had this man not conducted the ambush, then Bobby would have still lived.