Adam Armstrong struck late for Saints, with Everton having a goal for Beto denied by VAR. Dyche also felt Saints defender Jan Bednarek was lucky to stay on the pitch after hauling down Beto.
"We’d controlled a lot of the game,” explained Dyche. “We didn't need to use the ball as much because they have the ball, but they never really opened us up. When we did have it, I thought we asked questions of them, we got in key areas.
"It's not really a sloppy goal, we should score at the other end and they get a breakaway. Sometimes that happens from a misshapen team with plenty of desire to get back and they get a goal out of nothing really at that stage of the game.
"But the big key decisions went against us. The offside, that's fine because I believe in VAR on offsides particularly, but VAR's got to step in on the sending off. That's a sending off for me.
“The performance was solid enough today there were a lot of good signs, a lot of good play at times – certainly to make a lot of chances away from home. I always speak about quality chances. There was enough quality moments and quality chances and quality positions of course.”