Despite dominating the first half, Burnley found themselves going into half-time locked at 0-0, although they felt they should have been awarded a penalty when it looked like Ashley Barnes had been pulled down in the box.
The Clarets let referee Harrington know how they felt at half-time and within a minute of the restart the home side did win a penalty when it was ruled that James Coppinger pushed Sam Vokes.
Vokes stepped up and scored from the spot before Junior Stanislas made the game safe with 15 minutes to go - although it was the opener that riled Dickov.
"My thoughts are 'it is not a penalty'," Dickov said. "I did not think it was at the time and we just watched it numerous times and we still do not why it has been given.
"We have been told it is for a foul by James Coppinger. From the Burnley's player point of the view he has not gone down. There were no appeals, no nothing and the referee has given it.
"What I will say is I know Burnley felt they should have had a penalty in the first half and a few of their players and staff were at the referee in the tunnel so it's whether that has got to him or not.
"I am not going to take anything away from Burnley because I thought they were fantastic. They're a top team.
"For that to happen 20 seconds into the second half it is a massive, massive moment in the game.
"It's decisions at this time of the season where there is a lot to play as well that officials have to be getting right and it was quite clearly wrong."
However, despite Dickov's claims that Burnley influenced the referee, his opposite number was quick to insist that his players and staff had done nothing wrong.
Burnley boss Sean Dyche, whose side are now three points behind league leaders Leicester, said: "I thought we were good value again overall but Paul's
team came here nothing to lose everything to gain.
"I thought they gave us a very hard game and I thought we had to be resilient in the first half.
"I'm surprised because in the first half we have had an absolute stonewaller on Ashley Barnes so if you are going to look on the balance of play you haven't got one you've got the other.
"Our captain, as he is right to do, just suggested to the referee, 'why didn't you give a penalty?', he thought it was.
"I was absolutely right behind him, no bad language. He just said to the referee, 'I'm very surprised how did you not give that, it was a stonewall penalty'.
"Look there is frustration when people get things like that happen to them, we've had our own share of things not given for us so I understand Paul's frustration, I've been him on a number of occasions, but no there was nothing untoward."