The teams shared the points after their Scottish Premier League clash ended in a goalless stalemate on Saturday.
It was Dods who could have had the biggest impact on the game, when his half-volley smacked the underside of the crossbar in the first half before he saw his clearance skim against the post after the break.
In the end, Dods had no real complaints about the result which followed a 2-0 win over Hearts in United's opening SPL match.
He said: "The first one I caught well and the ball appeared to
be going in and caught the underside of the bar. I was hoping it would come down over the line but it wasn't to be.
"Then in the second half I was stretching to get something on it, it flew off my boot and luckily hit the post and came back out.
"I was disappointed in the first half and happy in the second half.
"We got off to a bad start last season and lost a few goals so to have two games and keep two clean sheets this season is great from a defender's point of view."
United are expected to be one of the main challengers for third spot in the SPL and were favourites heading into the match at the new St Mirren Park after such an impressive showing against Hearts last Monday.
"We were hoping we would stamp our authority on the game in the second half but we never really got on top," admitted Dods.
"They made it hard for us. We both had a couple of half chances without anyone really getting on top so it was probably a fair result.
"The way the game was going, one goal was always going to be the difference if it came."
St Mirren manager Gus MacPherson was also satisfied with the result, which saw Hugh Murray make his first appearance of the season after missing last week's 2-1 defeat at the hands of Hibernian with a groin injury.
"We took a chance on Hugh," MacPherson said.
"He has only really trained for a couple of weeks and had 60 minutes in a bounce game on Tuesday. But he gives us that physical edge in the middle of the park.
"He came in and, considering how little he had done, he did extremely well."