If you purchased travel insurance, then you need to file a claim for your additional expenditures. Since you purchased the air through Carnival and the cruise did you purchase the travel protection?
If not then write a letter to Carnival, keep it short and to the point about the delay and the fact that you only were able to join the ship for the last 3 days and explain why, with proof from the airlines, send it to the main address at Carnival in Miami with attention to the Research Dept. You might get a credit towards your next cruise, you never know. I have seen it happen. Try to keep the letter strictly to the facts, not a complaint letter against Carnival, after all it was not their fault the airline experienced mechanical problems. Again, if you purchased travel insurance file a claim on that also.