Eisenhower and Dulles believed that the action hurt the overall standing of the west in the region and would make regimes like Egypt and Syria likely to expand their ties to the Soviet Union. This would make it more difficult for the U.S. to further its containment of the USSR, as it sought to isolate the Soviets as much as possible. The U.S. also received a short term benefit as it increased popular perception of the U.S. in the region, though it's subsequent efforts to contain Nasserism eliminated the good-will bounty.

They also viewed the action as embarrassing to the United States and an attempt by Britain and France to recapture the sort of imperial glory that the U.S. was against. Dating back to WWII the U.S. aggressively used it powers to try to force both Britain and France out of their former possessions (there are obvious exceptions to this, see Vietnam for one) and favored an international trusteeship and gradual independence for former colonies. Britain and France viewed this with deep suspicion and accused the U.S. of employing economic imperialism in the guise of great power benevolence. That France and Britain undertook the operation without informing the U.S. beforehand indicates that they expected disapproval, but hoped to present Eisenhower with a fait accompli.

It's worth noting that Eisenhower came to regret his decision, as the US did not establish the sort of influence in the region he hoped for. He would look back and term it one of the great mistakes of his presidency.