They both foresaw consequences and cared but there weren't actually many great solutions available to them.

During World War I Britain had promised overlapping portions of the middle east to three different sets of people. In the Hussein McMahon correspondences it had promised an expansive independent Arab kingdom covering virtually all Arab Ottoman territory except Lebanon and Basra. In Sykes Picot Britain had divided that same territory up between itself and France. And in the Balfour declaration Britain had committed itself to establishing a Jewish National Home in Palestine.

The Balfour declaration is a good example of how they understood that there could be problems. It contains the line "it being clearly understood that nothing shall be done which may prejudice the civil and religious rights of existing non-Jewish communities in Palestine". Clearly then they understood that the creation of a Jewish national home could prejudice those civil and religious rights. They simply believed that they could come up with solution that didn't right up until 1937 when the Peel commission called for partition for the first time.

Or take Iraq. There was actually a Shia and Kurdish revolt against British rule in 1920. They understood just how much of a powder keg the country was. They believed (by which I mean the British involved in the issue, like T.E. Lawrence, Gertrude Bell, Percy Cox etc), however, that immediate Arab self rule would probably end in disaster. They knew that their task was to create states and nations where there had been none before.

The calculus in doing so in Iraq, for instance, was not so much divide and rule as it was to balance competing interests against one another, with King Faisal as the font of national identity, in such a way that the competing factions would be forced to rely on one another. I actually think the focus on ethnic/sectarian balance actually ignores just how much the British screwed up social class in Iraq. They basically enacted land reform in a way that granted tribal sheikhs unprecedented wealth and power at the expense of tribesmen who were now legally reliant upon their tribal sheikh (who was now also for the first time their landlord as well) for sustenance.

French policy was probably worse and was a much more standard from of "Divide and Rule" as they created confessionalism in Lebanon. (It's interesting to me, in regards to Iraq it seems that the implication is that the British should have taken account of Shia/Sunni differences by enacting something like confessionalism, without remembering that cofnessionalism has probably produced a more disastrous set of circumstances.) And they divided Syria into four between Damascus, Aleppo, Jabal Druze, and an Allawite state.

They did this, however, on the model of Morocco, which is of course actually one of the more cohesive and peaceful post-Colonial states. That said they clearly knew that they were imposing a system the people didn't want. The King-Crane commission cataloged the views of Syrians in extensive detail and the Syrian National Congress explicitly rejected French advisement, instead they actually requested American assistance, and barring that, British.

edit: the above summary, reading it back, also actually focuses entirely too much on European aims and wishes while ignoring some of what the local people wanted. In Iraq, for instance, it's worth noting that there was an actual nationalist demand, exemplified by the Ahad, or Covenant, movement to form a state out of the Vilayets of Basra, Baghdad and Mosul that form modern Iraq. While there was some haggling over the boundaries, particularly over Mosul, I don't know of any movement for Sunni separatism like we see in Iraq today. Kurdish separatism, yes. But there was never any real consideration of splitting off the modern "Sunni Triangle" into Jordan or something like that, so I'm not convinced that Iraq, with the exception of Kurdistan, would actually look that different if the local populace itself had formed the borders.

Syria is a different beast entirely. The Maronites of Mount Lebanon being probably the only group in the Middle East that actually wanted foreign rule. But if King Crane is any indication, barring French/British intervention Syria would have been much larger and included Palestine and Lebanon as well, at the least.

The book 'World Poverty' by Harold Kerbo discusses how, as Europeans colonial powers divided up Africa, Southeast Asia, and the Middle East, they purposefully included tribes who had traditionally fought each other within the same countries. The purpose was to encourage civil war and infighting so the colonized peoples wouldn't come together to overthrow their new leaders. This unfortunate policy was a major cause for centuries of war and poverty around the globe.