The pilots of the Ninth Air Force (the Tactical Air Force assigned to the US First Army) could see the hundreds of assault boats in the water, heading towards the beach. They did not want to bomb their own boats, so most, if not all, of them decided to wait a few extra seconds before dropping their bombs. This meant most of the bombs landed in the fields behind the hills beyond the beach, killing hundreds of cows, but very few Germans.
Source: "Overlord- General Pete Quesada and the Triumph of Tactical Airpower in World War II" by T H Hughes

The issues with using air power in direct support of troops (Close Air Support) during D Day comes down to a number of factors, but the most important ones are accuracy and concentration.

Accuracy Heavy bombers (eg Lancaster, B17, B24) could carry the sort of bomb loads which could devastate a defensive position, but only 50% of bombs were likely to drop within a 400m radius of the target – utterly unsuitable for Close Air Support. Even the most experienced, highly trained crews could only reduce this to 100m. Smaller aircraft could be more accurate, but with lower yield weapons which leads us to concentration.

Concentration With smaller yield weapons (light bombs, rockets, cannon), more hits are required on a target to achieve an effect. This takes more time and increases considerably the number of ac being put at risk – this was identified as a major problem for German JU-87 aircraft during the Battle of Britain. /u/davratta has commented also on pilot’s actions: Close Air Support is difficult to pull off and requires highly trained and experienced aircrew and well-practiced coordination with ground forces. This is as true today as it was 70 years ago and the more sorties you fly, the greater the risk of fratricide.

It is easy to see Air Power as a panacea, hooning around at 10,000 ft raining death from above and carving a swathe through enemy defences. The reality, even in modern warfare, is very different – air attacks against fixed defences ahead of D Day had limited effect with many cruisers forced to divert fire support on the day in order to suppress coastal batteries which air attacks were intended to knock out.

/u/CanadianHistorian has touched on the subject of deception. Saturation bombing of Normandy would have given away the location of the invasion and afforded the Germans the opportunity to reinforce defences. In order to prevent giving way the intended landing grounds for every mission launched in the OVERLORD area, one would be launched against a non-OVERLORD target. This was part of the highly successful deception campaign for the invasion, Operation FORTITUDE.

Where Air Power excelled, however, was in Air Interdiction: disrupting enemy lines of communication well behind the battlefield. With air superiority over North Western France, bombers of all kinds could attack railway lines, bridges, marshalling yards, rolling stock and depots with relative impunity. The effect of this was to disrupt logistic support to German units in the OVERLORD area, but also to delay the deployment of Rommel’s operational reserve once the invasion had begun. FORTITUDE ensured that the operational reserve was kept well away from the coast in order to respond to a number of potential beachheads; air interdiction delayed the deployment of the reserve to D+2, more than enough time to establish the beachhead.

According to the "D-Day Museum" the Allies landed 156k troops in Normandy on June 6, 1944. While there were no official casualty lists for DDay itself the generally accepted number was 10k which included 2500 dead. Newer research has put the casualty figures higher which include around 4400 dead. However, that also includes the airborne.
http://www.ddaymuseum.co.uk/d-day/d-day-and-the-battle-of-normandy-your-questions-answered#troops

So in actual fact the casualties suffered by the Allies on DDay were actually quite low. The vast majority of Allied soldiers on DDay got off without a scratch. It's not quite the bloodbath people tend to picture it as, which I would imagine is possibly due to movies such as Saving Private Ryan and its 30 min starting bloodbath.

In addition to the other answers, it should be pointed out that there weren't actually any Germans on the beaches. They were 500 yars away in prepared fortifications. Getting troops on the beaches was no problem but assaulting those fortifications was. The infantry was supposed to have amphibious tanks with them for this purpose but they sank.

Bombs being dropped within 600m is considered "danger close" in other words, good chance of you hitting your own guys. The second reason is the germans did have significant amounts of AA batteries in that event. The idea was to drop paratroopers behind enemy lines the night before have them clear artillery and anti-air and have the short range bombers and fighters fly missions throughout the landing to protect the troops. Either way a lot of those bunkers were very, very well built and could withstand the bombardment.

They did do quite a bit of schwacking with the big guns on the naval ships, but things don't go to plan and the assault had to continue as it was. Eventually the AA and the Artillery was taken out (band of brothers show this quite well) and it allowed bombing runs to take place more often and effectively.