The referee should have told you at the end that you have a right to appeal and told you how many days you have to make that appeal. If you want to appeal and cannot afford to hire a lawyer, the court may appoint you an appellate attorney to appeal your sentence if you feel that it is unfair. It is a hard threshold to overcome and I doubt you would probably be successful given the facts you stated, but you can always have an appellate attorney look at it to see if there are any issues that can be brought up on appeal.
You should have been provided with your appeal rights. If the decision was made by a referee, you usually have a right to have that decision reviewed by a judge. The referee only makes a recommendation that is then ordered by the judge.
You have a right to appeal the sentence. I would guess that the Referee or Judge sentenced you without considering the false statements. At least that is what they will say.