CLRS is not a software engineering book, it's an algo book. This is a somewhat widespread misconception. Anyway, what language are you using to implement these algorithms? Some languages are much worse suited for doing algo work than others. I always hated implementing even the simplest algos in C or Python but it's actually kind of fun in Swift, Rust and Haskell (the types really do help in cementing your understanding of what's going on).
You should try doing that. Write an algo one day and get as far as you can without looking for help. When you are done check your solution against some correct solution. Do it the next day again and try to do it faster. Repeat a couple more times like next week, next month and before you know it, it will be second nature.
Also, there was an article yesterday on HN about how the process of mastery is about memorization and repetition https://news.ycombinator.com/item?id=12508776
You should try doing that. Write an algo one day and get as far as you can without looking for help. When you are done check your solution against some correct solution. Do it the next day again and try to do it faster. Repeat a couple more times like next week, next month and before you know it, it will be second nature.