すまなく is 'sorry' but how does 思うが change this meaning? 'I feel sorry?'
すまない = sorrowful
すまなく = sorrowfully (this is the 連用形 of すまない)
思う = to think (verb)
が = but (conjunctive)
Literally すまなく思うが = I think sorrowfully but... = I feel sorry but ...
The sentence is unfinished. It is up to the reader/listener to guess what follows.
Here the meaning of 思う is ratherr "feel" than "think" in English.
すまなく思うが＝ Though I feel sorry,...