Awkward can also mean 'difficult / complicated', which I think is closer to this case than 'embarrassing.' The word can also be used to describe the general mannerism(s) of an individual. He is very awkward when it comes to mechanics.
Thank you, Philip. I have another question: When awkward is used in the sense of embarrassing, is it really equal to embarrassing? Is it stronger / weaker than the feeling of embarrassment? Are there situations where the two words are not interchangeable? For example, let's use this sentence: "It was so awkward when he started singing".