Yes, the 1040 and the 1040NR are very similar but there are a few differences that affect the deductions, credits etc. so you may be short on tax (very bad because the IRS will charge interest and penalties, or you may be due more refund (Either way accurate is always better when dealing with the IRS as they can be in-forgiving). Also, there are other difficulties that will come up as well- possibly with USCIS when you have to renew. The way I see it: you made an honest mistake with no bad intentions and you did file and pay taxes which is your responsibility, the best thing to do is correct the errors now rather than later.
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