Funny how the conclusion now is that the LW should've concentrated more on bombers in NA, the same directive that led to her quick demise over France and Germany a few years later. Of course whenever that scenario is discussed everyone is quick to point out how stupid Goering was by concentrating on attacking the bombers. But it doesn't matter, the goal seems to be more in line with "if Marseille wasn't a liar he was at least an arrogant prick with no regards for the life of his comrades on the ground".
Oh concentrating on bombers is the correct strategy. Bombers cost more resources, have larger crews and damage people on the ground. If you sacrifice 1 fighter for 1 bomber then you will win if you productive capacities are similar. Since the US's was so much larger they needed somewhere between 3-5:1, which they achieved easily in '43.
In mid-late 43 the Luftwaffe won the battles with both the USAAF and the RAF, scoring strategic wins. The 8th pulled back to within escorted range and only re-attacked when they had long range escorts. BC pulled back too.
But, the Luftwaffe's successful tactical doctrine was very vulnerable to ecort fighters. They depended on heavy twins (110s and 88s) with rockets and heavy cannons to break up formations, then the single engined fighters could take out the stragglers and the now less well protected groups.
But those twins were far too slow to exists in daylight in contested airspace. Once the ranges of the US fighters grew, they were taken out of the equation. This is where all those poor decisions made prior about single engined fighters came to haunt them. Firstly they didn't have enough. The 190s altitude performance was poor, made poorer if heavier cannons and/or rockets were fitted.
The 109 had the high altitude performance, but not if you loaded it up with 30mm cannons and the like.
And without those they didn't have the firepower to quickly take the US bombers down (estimated it took 20 x 20mm shells on average, vs 3-5 30mm ones).
Now if they had enough fighters, they could have done both, with lighter ones for combat against the escorts, while the up-gunned one slipped through to hit the bombers. But they didn't have enough to do both successfully.
So when the '47s and 38s upped their range they hammered the twins, the Mustangs were the coup de gras and finished the job on the singles.
The lack of numbers killed any chance of applying many obvious tactics, like squadron sized intercepts of the rendezvousing fighters, well before they linked up, to force them to drop their external tanks and hence not being able to complete their escorting.
So the bad decisions made in 41 and 42 on fighter types and production numbers (and pilot training) meant they were unable to respond. Their lack of a fast twin meant that they had nothing that could survive in daylight in contested airspace and the loss of that meant crippling the single engined fighters performance to carry the guns necessary.