Ashley Barnes gave the hosts the lead mid-way through the second period, but a late controversial goal from Manolo Gabbiadini rescued a points for the Saints.
Speaking after the game, Dyche admitted that he was left frustrated by the result and claimed that his side did enough for the victory, as quoted by the club's official website.
FULL TIME: Burnley 1 - 1 Southampton.— Burnley FC (@BurnleyOfficial) February 24, 2018
Dyche said: “I thought we did enough to win that game, but there was stuff out of our control, which is really frustrating.
“Without being brilliant it was a nice, solid performance, but it’s a tough one to take because we’ve not had much go for us during the game."
The equaliser was surrounded by controversy as first referee Bobby Madley got in the way and Burnley lost the ball, and in the same move it appeared that the goal-scorer Gabbiadini fouled Kevin Long and it's fair to say that Dyche was angry at the referee's decision not to give a foul.
Burnley v Southampton - possibly the lowest quality Premier League match I've ever seen— Simon Peach (@SimonPeach) February 24, 2018
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“It’s hard for referees to try and get out of the way of everything, but my point is if you are the referee and you have just put them on the counter attack, then see a defender pulled in the box, I think as a referee my decision would be that is a foul, because it’s cost a team a goal.
“So, for them to get a goal out of a nothing situation and us to lose two points on the back of that is very frustrating."
The draw means that Burnley have gone 11 games without a win in the league, but despite their current downturn in form they still remain seventh in the league and safe from relegation.