The Clarets remain rooted in the relegation fight and have now won just one of their last 11 Premier League matches.
Despite generally having the better of the play and creating chances for the likes of Ashley Barnes, George Boyd and substitute Sam Vokes, Dyche’s men never truly convinced in their battle to break the deadlock.
Barnes had been given a rousing reception by the home fans after a week in which his challenge on Chelsea’s Nemanja Matic made headline news.
But it was Swansea who left Lancashire with maximum points following a chaotic own goal, goalkeeper Tom Heaton and Kieran Trippier combining to??fumble the ball over the line midway through the second half.
“I don’t think there was anything between the two sides,” Dyche told Sky Sports. “Both teams played to win, but there was a little bit of flatness to both sides and maybe that was down to the furore all week.
“Generally the margins are tight and we let in a real soft one again and of course we have got to make sure we eradicate that.
“I thought it was going to pan out as an indifferent 0-0 because no team could find that defining moment and there was no real zip about the game today.”
Dyche shrugged off two failed penalty appeals for his side and preferred to stress the positives, insisting Burnley remain very much in the running to survive.
Dyche added: “You can’t guarantee anything in the Premier League and when you look back at the start of the season a lot was made of us not winning any of our first 10 games.
“If you win games the table looks after itself. There is a lot of football still to go and considering where we were after game 10 I think we are making a good fist of it.”