The British retreat from Mons, WW1, was outstanding, however. When the French withdrew and German numbers meant the BEF would be encircled, they slipped off at the last moment and retreated in an orderly fashion with the Germans hot on their heels. The Germans were extremely impressed with the British Army during and after the Battle of Mons, which wasn't what they were expecting (the phrase they had used prior to Mons was: "contemptible little army", which is how and why "The Old Contemptibles" was borne). The Germans considered Mons to be a temporary defeat and British soldiers couldn't understand why they were being ordered to retreat as they felt they were getting the job done. What they didn't know was that the French had a made a decision to withdraw exposing one of the British flanks.
The problem with Mons isn't that the British didn't do well, but that it didn't matter, and worse – considering the overall strategic situation – the British had no business taking the risk of allowing themselves to get caught in a fight with a vastly numerically superior foe. That's why there was an organized general retreat was the business of the day. The British were taking an unwanted and unnecessary risk, and not just for themselves.
But they were good, so thanks to good soldiering the BEF managed to break off the engagement and slip away. It doesn't however remove the problem that it was still a pointless piece of risk taking to allow yourself to get locked in a fight with the enemy like that. The BEF could make no positive difference by picking that fight, and had they failed to get away the Germans would have destroyed them wholesale opening a BEF-sized hole in the French lines.
Joffre was busy detailing French troops to screen the BEF so that would at least get some kind of heads up if they decided to vacate the war entirely. As was feared from looking at their ardent retreating away from from frontline and the French army.
It's also telling that the Germans at the time did in fact not quite notice Mons. It just got rolled into the massive general fighting they were doing. It's why we can't get corroborating German figures for the battle – the army just noted down the casualties in a continuum of fighting, and so in retrospect we can't separate out Mons. Which means it's just British estimates, since we can't separate out Mons from the general fighting in the German sources.