I have noticed that undervaluing yourself is likely to work the opposite way. People will think you aren't good enough to command the salary they had in mind.
Bear in mind 4-5 rejections is not many. Depending on the economy and the hiring at the time I have looked I have gotten offers from the first interview or not even gotten an interview until I sent out over 100 resumes (I graduated in a very bad year for entry level hiring). And hiring is a competition, if you continually get rejected for the same level jobs, you may be applying for jobs at the wrong level. If you want to be a senior whatchamacallit with 3 years experience, you had better have a lot of accomplishments to show to compete with the people who have been senior whatchamacallits for ten years.
Now what you can do is try to figure out if you can improve your interviewing skills. can you see a pattern to the questions that you didn't feel you did well on? Are they the hard skills questions or the soft ones? Did you just not know the answer or did you get to nervous to remember it? Are you failing to sell your strong points?
Like anything else interviewing gets better with practice. So practice by writing out all the questions you can think of that people have asked (and any others that you woudl ask someone if you were interviewing them for the position you want) and then video yourself answering them and do it over and over again until you improve how you present yourself and until you can answer the questions relatively easily. It's painful to practice by videotaping but it is hands down the best way to improve if you are serious about getting better at interviewing or public presentations of any kind.