The Hornets took the lead on 11 minutes, when, after a succession of corners, Nathanial Chalobah struck a sweet volley from 15 yards out through a crowd of players and past Lee Grant.
But the Clarets levelled through Charlie Austin's 22nd of the season, which came from the penalty spot, and the hosts saw a host of chances go begging after that against Dyche's former club.
They had a penalty appeal rejected in the 74th minute after Dean Marney's shot was deflected into Marco Cassetti's hand. And Joel Ekstrand's superbly-struck effort from 25 yards hit the bar.
"We're not hard done by because that is the reality of football," said Dyche.
"You can dominate games and create as many chances as we did and still not win and that was the obvious view of the game.
"I was pleased with the reaction because I thought it was terrific. From that moment onwards I felt we dominated and the chances we created, I've lost count.
"It was a penalty, I've seen it again (the first one) and I was disappointed not to have another one in the second half because it looks like a clear handball and I don't know how it wasn't given.
"That aside, I am more interested in the performance, which I thought was very good again today.
"The reality is though that we have to turn those performances and chances into clinical moments which change games. We so nearly did but we found a keeper on top form."