Another Liverpool man, 20-year-old Graham Sankey, later made a signed confession to the attack, but the evidence was rejected by the Bulgarian court.
Mr Shields' father, also called Michael, met Mr Straw at the Foreign Office in London.
Speaking afterwards, Mr Shields described the meeting as "positive" and said Mr Straw had promised to speak to his Bulgarian counterpart.
He said: "I was fairly happy with the way the meeting went.
"The most important thing is that Jack Straw appeared to take it seriously, and he said he would speak to his Bulgarian counterpart on Michael's behalf."
