Rhodes' lucky goal broke Burnley hearts again with his second goal in three games between the two clubs, after the Clarets took the advantage following some neat build-up play and a wonderful strike by Junior Stanislas.
Dyche felt his side did well to deal with the threat of Rhodes for the majority of the game, but were unlucky when it came to the Blackburn goal.
"We had a number of chances to get the ball away - it's a momentary thing and Rhodes gets an unbelievably lucky finish in a game we deserved to win overall," he told Sky Sports.
"We played them here last year and drew 1-1, but he only had four touches all game and scored. To be fair he's read it early but you're not expecting a goal from that position.
"I thought in the first half we were excellent, we kept the ball and created chances. In the second half Blackburn went more direct and it became a bit more like a derby and we didn't secure the ball as well as I'd hoped."
On Burnley's goal, Dyche said: "It's great when your substitution comes off, Danny Ings has set him up brilliantly and it was a fantastic finish from Junior and on another day worthy of winning the game.
"We thought we had the win today, it was a strange moment that cost us again, but one day it will turn. I don't believe in records, I take each game as it comes."
Dyche was also left to rue another of the game's major talking points following the sending off of Lee Williamson for deliberately bringing down Ings as the striker went through on goal.
He said: "Unfortunately Williamson's challenge will get a pat on the back from his team-mates, he's taken one for the team. It's a sad part of our game in reality but it's the professional side of the game we've seen there."
Gary Bowyer acknowledged Lady Luck was smiling on Blackburn's side of the M65, but also thought his young team were worthy of the point.
"When we go 1-0 down with 10 minutes to go, and the average age of the team was 22, you do wonder and question how they're going to react," he said.
"But, in this environment, we've got nothing but praise for them because they came back with a fantastic attitude and spirit, and in my opinion fully deserved the equaliser."