The table topping Bairns needed a second half Anton Dowds strike to salvage a point after Dumbarton had taken a shock lead through Rabin Omar.
Falkirk defender Mark Durnan was red carded late on for a last man foul. And Miller felt the number five should have earlier won a penalty for a foul on him following a corner.
Miller said: “I thought we were a wee bit sluggish today.
"We were disappointed with the all round performance, albeit the goalie makes incredible saves at the end.
"The one Durnan gets dragged to the floor I thought was a stonewall penalty. He’s up to try and win the header, the boy’s fallen over and he’s dragged him down with him.
"I thought the linesman had a good view of it but we’re not complaining. We’ve come away with a point where we’re down to 10 men and fighting for everything in the last 10 or 15 minutes.
"For the sending off he’s just tried to kind of shield him, I don’t know if he caught him or the striker’s been cute and gone down.”
Falkirk now face a massive Scottish Cup third round tie at Celtic this Saturday.
Miller said: “We’ll go there and enjoy the occasion.
"We’ve got nothing to lose. Obviously we’ll make a good few changes as well with players that need game time.
"It will be a good occasion for the boys. A lot of them haven’t played at Celtic Park.
"We will hopefully play a decent brand of football.”