The Brecon and Radnorshire MP was fined £1,500 and ordered to carry out 50 hours of unpaid work for submitting two false expenses invoices for landscape photographs to decorate his new office
He now faces losing his seat as a recall petition is set to get underway.
Mr Davies has written a lengthy statement online, claiming he was the victim of a "technical breach of a complicated accounts process."
He explained: "This has been a very difficult period for my family, my staff and myself.
"At no time did I intend or attempt to make any form of financial gain from my actions and this has been confirmed by IPSA, the Metropolitan Police, the Crown Prosecution Service and the Judge. Indeed they all recognise that my mistake cost me £700 that I could have claimed quite legitimately – sadly it has cost all those to whom I owe my loyalty so much more in emotional terms.
"I made a technical breach of a complicated accounts process and fell foul of a new law which is unique to Members of Parliament. However, the Act is binary and my mistake is an offence, albeit arguably one without victims.
"I wish I had not made this mistake and that I was aware of every aspect of every law but unfortunately I am also capable of making mistakes and mine has been a very costly one.
"I am extremely saddened that this has happened and I apologise once again to all my constituents for making such an error."
The two charges related to the period when Davies was setting up his constituency office.
He bought nine images from him to decorate and display in his constituency office, using his own money to pay the £700 for them initially.
There were two budgets available to him, the Start Up Costs Budget - for office furniture and IT equipment - and the Office Costs Budget, both of which he could claim the full amount from.
But during the sentencing hearing Philip Stott, prosecuting, said Davies found in February 2016 that only £476.02 was left in the Start Up Costs Budget, with £8,303.75 remaining in the other.
He then created two fake invoices, so the £700 cost could be split between the two budgets - £450 to the Start Up and £250 for the other.
Mr Davies will now hold surgeries in Builth Wells to explain the matter.
He said: "Any constituent who requires further clarification on any aspect of this case, I would be more than happy to discuss it with them in person and also to provide whatever documentation they wish to see, as all my affairs are completely transparent.
"Therefore I shall be holding open surgeries in my Builth Wells constituency office from 10am – 4pm on Friday 3rd and Saturday 4th May, together with Friday 10th May and Saturday 11th May, where the photographs, accounts system etc will be available to view and where I will happily discuss this or any other subject of concern to my constituents."