The Clarets started the better of the two sides, taking advantage of a sluggish Southampton, while goalkeeper Joe Hart was once again in inspired form as the England international claimed his second consecutive clean sheet as he starts his Burnley career off in brilliant form.
Speaking after the game, as quoted by Burnley's official website, Dyche said: “I was certainly pleased to come here and dominate for periods of the game, away from home.
“Result wise, it was a winning draw, as one of my old managers used to say. Also, in competitive games recently, we’ve had three of the last four away from home and all the demands, mentally and physically, that come with that.
“This has always, historically, been a tough place to come and I thought we dominated good spells of the game.
Dyche was pleased with the mental strength shown by his players also, claiming that his side had done enough to warrant walking away with all three points.
“I was delighted with the application and attitude and when they came into it, we defended resolutely and did the job we had to, to get a well-deserved point.
“We’ve done enough today to come away with a victory. Their keeper has made two very good saves and at the other end, top players don’t allow a keeper to make a save and we continue to mature into that, so there were so many good things today.”
Burnley face the second leg of their Europa League clash with Turkish club Istanbul Basaksehir on Thursday, after having played a goalless draw out in Turkey last week. The Clarets then face Watford at Turf Moor on Sunday.