In the first ever match between the sides, Cody McDonald's early opener was cancelled out by a Richard Hinds header at Huish Park as both sides shared the spoils.
However, the visitors, playing their first game in the third flight of English football in 48 years, thought they should have been awarded a late penalty as McDonald tangled with Byron Webster.
Thorn said: "Cody McDonald could have had a hat-trick. He was pulled down for a penalty and on another day you never know. We created enough chances to win the game. I've seen it on the video and it's a blatant penalty, but we're pleased to get the season underway.
"The first half was a typical first game of the season where everyone was a bit on the edge, and the occasion got to us. When we scored I thought we settled down, but we are very disappointed with the goal we conceded.
"I didn't think we really played at the top of our game, but still created lots of chances, so that's encouraging. It's a point away from home on the first day of the season against a tough team. Now we need to kick on."