No, it should be "I couldn't do it" For example: Did you clean up your room? No, I couldn't do it because I was ill.

i couldn't DO it. could/should/might/can/shall/may + infinitive

Thomas: Please memorize this easy rule, and you will NEVER be confused again: ALWAYS use the base form (the infinitive with no "to") after so-called "modal verbs": I CAN do it. (cannot do) I COULD do it. (couldn't do) I MAY do it. (may not do) I MIGHT do it.(might not do) I MUST do it. (mustn't do) I SHALL do it. (shall not do) I SHOULD do it. (shouldn't do) I WILL do it. (won't do) I WOULD do it. (wouldn't do)

or it can be"i can't do it.