In the Battle of Crete in 1941, the numbers were around equal but the British have supremacy in the sea and in land equipment. The only advantage the Germans had was air supremacy. So why did the British surrender their forces?
Actually most of the defence force was successfully evacuated, not surrendered.
From Winston Churchill's The Grand Alliance, Chapter 16:
General Wavell to Prime Minister, 27 May 41:
1. Fear that situation in Crete most serious. ... There is no possibility of hurling in reinforcements. ...
2. ... Such continuous and unopposed air attack ... makes administration practically impossible.
3. Telegram just received from Freyberg states that only chance of survival of force in Suda Bay area is to withdraw to beaches in south of island, hiding by day and moving by night. Force at Retimo reported cut-off and short of supplies. Force at Heraklion also apparently almost surrounded.
4. Fear we must recognize that Crete is no longer tenable and that troops must be withdrawn as far as possible. ....
and from German XIth Air Corps after action report [ibid]:
.... The area of operations on the island had been prepared for defence with the gravest care and by every possible means. ... All works were camouflaged with great skill. ... The failure, owing to lack of information, to appreciate correctly the enemy situation endangered the attack by the XIth Air Corps and resulted in exceptionally high and bloody casualties.
The collapse of the defence around Canea, Maleme, and Suda Bay meant that a solid beachhead had been established by the Germans at the west end of the island, upon which seaborne reinforcements could be landed by the Germans (as Italian forces then did hile the British evacuated).
Unlike Malta, no provisions had been made to station RAF fighter squadrons on Crete and the island was at the very limit of Spitfire range from Egypt; allowing only the briefest of time for pilots to attempt air combat. This was attempted, but proved ineffectual. The Royal Navy suffered significant losses during the few days of battle and evacuation as it was, and any attempt to supply the island long term under the weight of overwhelming German air superiority would simply have increased both ground and naval casualties, for only a slightly delayed same result.
To summarize: The defenders were low on ammunition and food, with all their remaining heavy equipment (after the recent evacuation from Greece) disabled by the Axis air attacks. The attackers were now able to resupply and reinforce by sea under strong air support, while the defenders were no longer able to reliably provide any resupply or reinforcement. The defenders' line had been broken, such that they were in danger of being surrounded (where they were not already surrounded). Freyberg to Wavell, May 26, [ibid]:
The troops we have, with the exception of the Welsh Regiment [1 battalion] and the commandos [2 companies], are past any offensive action.
These are certainly circumstances when it is reasonable to evacuate, and live to fight another day.
Royal Naval losses in the vicinity of Crete between May 20 and June 1: three cruisers and six destroyers lost, one battleship out of action for three months, several other ships damaged sufficiently to reduce combat effectiveness and speed. Those losses resulted in the destruction of the German Paratroop division as an effective fighting force, a significant achievement, and the successful evacuation of most of the remaining Crete garrison. That was thought to be sufficient, and I agree.
If the Commonwealth "surrendered prematurely at Crete," it was in the fighting around the Maleme airfield.
On the first day of the battle, the German paratroopers were decimated as they tried to land in Crete. A number of survivors were concentrated west of the Maleme airfield, defended by, among others, the 22nd New Zealand battalion.
In the battlefield confusion, this battalion was split into two groups, call them the west wing, facing the main German concentration to the west of the airfield, and the east wing around the airfield itself. Fearing that he had "lost" almost half his force, the battalion commander asked for reinforcements, which were denied. Then he asked for permission to pull back his exposed (east wing) half-battalion, which was given. When the west wing found itself totally exposed by the pullback of the east wing, it also withdrew. These two actions enabled the Germans to capture the airfield, basically by a strategy of "divide and conquer."
The Germans had lost about half of a "reinforced" paratroop division in the initial assault, but it was able to fly in a mountain division after capturing the airfield. These two divisions, which had more heavy equipment and air support, overwhelmed the defenders (one "mainline" New Zealand division, one reserve Commonwealth division, one second-line Greek division, and assorted other units).
Without the "premature" loss of the Maleme airport, Crete might not have been conquered.