The home side were celebrating their 150th anniversary but the visitors spoiled the party by coming out on top in a game that struggled to ignite.
After Jimmy Gopperth and Rhys Priestland had scored three penalties apiece to tie things up at 9-9 at the break, the Bath forwards started to gain the ascendancy and substitute Freddie Burns made their advantage count with his right boot.
Semesa Rokoduguni's late try made the game safe and Blackadder was full of praise for the way his team ground out their victory in Coventry.
"We made tackle after tackle and we had to do that. We didn't build enough pressure with the ball but we managed that defensively," Blackadder said.
"We kept ourselves in the right and I thought it was good. There are a lot of things we can get better at though and this was a real arm wrestle. It was tight and could have gone either way."