"Southampton are a big club with some big players and we have more than matched them at the end," Dyche said after the 4-3 loss.
"We were still going at it at 4-2 and 4-3 and right to the end. One of our biggest mantras is to have no excuses, no fear and no regrets.
"We play, as we do, and we come off the pitch knowing we have given everything and I thought that was absolutely evident.
"I am so pleased for the Burnley fans who travelled down because, once again, they have seen their team giving everything to win a game.
"It's a strange one to lose a game and have a feeling of pride and that you have done everything to win it, but that's a really good mindset for us.
"We have shown that many times this season and that's what we take from this game, because we kept at it and were relentless.
"The harshness of the business is you don't always get what you deserve.
“We possibly deserved a little bit more and didn't get it, but if you perform like that often enough you win more games than you lose."