The 19-year-old recently completed a three-month loan spell with the York Street club, having impressed The Pilgrims boss with his displays during the 11 matches he played for Boston.
Thompson was keen to sign the teenager on a permanent basis and tabled an offer to the defender but McCarthy opted instead to stay at Maine Road.
"It is a disappointment Paddy hasn't accepted the deal we put to him, but it's his decision and we must respect him for it," Thompson told the Lincolnshire Echo.
"It was a big decision for him to make. He's only 19 and didn't feel it was 100 percent right for him to come back at this stage.
"He did an excellent job for us in the three months he was here, but I would like to wish him all the best.
"You never know, maybe something can be resurrected in the summer."
Meanwhile, Boston are likely to miss Lee Thompson for the rest of the season after the midfielder had an operation on a injury problem just below his knee.
The recovery time for such an injury is estimated at 12 weeks and will take Thompson into the summer, by that point.
In other news, Jamie Cook has joined Conference side Stevenage Borough, who took over his contract.
