A goal each from strikers Darryl Duffy and Jo Kuffour in a 10-minute first-half spell sealed the points for the visitors, who were without leading marksman Rickie Lambert through injury.
A dejected Adkins said: "This was a chance missed for us to strengthen our promotion challenge. We conceded two really bad goals and couldn't recover.
"For whatever reason, we couldn't reach the sort of tempo we wanted to play at. But we still had 21 efforts at goal and it's disappointing we couldn't make any of them count."