German divisions running amock after penetrating a completely undefended front, the Ardennes (well, ok, a front lightly held but then abandoned) hardly implies an tactical mastery over their opponents but rather a case of the victory of strategic thinking.
As further proof of this, you have a large German armored force pouring behind your lines but you have massive forces both to the North of this penetration and south of it so as the defender what do you do? Me, I trade ground in the north and counterattack from the north and south to attempt to pinch off this German force and encircle them. In fact, this was the Germans greatest fear but given the fact that no one on the strategic level of the Allied command was thinking clearly by this point, it naturally did not happen.
To give the historic timeline of the panic events, on May 15th, Paul Reynaud, the French prime minister, phoned Churchill and told him that the battle was lost and that his country was defeated. Churchill and his High Command took this at face value and began plans to withdraw the BEF from the continent on May 16th. This withdrawl left a new massive section of front open for the Germans to pour through and effectively doomed the Belgian Army (the Belgians held the coast along with the 7th French Army, the BEF held the middle and the French the rest). Once this withdrawl began and effectively removed the Belgian and British armies from the campaign, things were pretty much over. Mind you, the Germans weren't even close to the Channel on the 15th and already French was defeated. Too bad no one told the French Army that they were defeated and saved them the 100,000 killed they would take over the next month.
Let's apply typical myths of WW2 on the Britsh side. They had no choice to withdraw as the French had given up and the Germans had them completely outclassed (and in the earliest accounts vastly outnumbered as well, a hold over of WW1 mythology). Moreover, not only were the French beaten and quitting but the BEF itself was poorly equipped and trained (outright lies given that the BEF was the only completely mechanized army in the world), its officers with no idea how to deploy armor while on the other side the Germans motored along French roads like herds of buffalo because as we know, only the German knew how to deploy armor which is true if we ignore the Franco-German armor clashes in various battles.
Of course, we need to look at facts and the facts are very disturbing. At Gembloux Gap, the Germans essentially had an entire armored division destroyed. It's a pity we never hear about this battle but it hardly fits the mythology of the war with the French employing combined arms tactics against the Wehrmacht and over the course of a two day battle (without any air cover, mind you) emerging victorious but were then withdrawn. In another armored clash the German lost the equivalent of another armored division. German superiority in armor and armored tactics hardly fits the evidence. On May 31, German armored losses were at 50% and bomber and fighter losses at 40%. This hardly fits into the idea of Blitzkreig!
This isn't to say the Allies didn't have losses but when one considers that the major Allied forces were untouched by combat that the bulk of the RAF and French Air Force had yet to be committed to action (unlike the histories that say it had been destroyed on the ground by the Luftwaffe per the Blitzkreig mythology) to say that the Allies had lost by May 16th is proposterous.
"Great events often have simple causes. In this case the cause was Churchill's acpuiescence to Reynaud's panic, a decision that brought the curtain down on one of the most discreditable periods of the European democracies and was the culmination of two years of betrayal and capitulations. Here were two leaders who could, if they had stayed the course, have fought Hitler to a bloody stalemate. Instead they panicked, Churchill no less than Reynaud."
This is key thing about WW2, if it doesn't fit in the fairy tale it is convinently disregarded and forgotten. The lies have been told so often though that it had become truth and anyone saying otherwise is a fool.

"The Allies deployed their armor wastefully in support of the infantry" or "in penny-packets" as British historians love to state it. Given that the BEF didn't even have an armored division deployed in France this is a truthful statement but it is certainly false when applied to the French but it doesn't fit the story and so it is discarded.
You must remember, the first casuality in war is the truth.