Dyche praises players' mentality in away draw at Hull
Tom Huddlestone put the Tigers ahead in the second half with a penalty, harshly awarded for handball against Michael Keane.
But Keane slammed in a quick fire equaliser, before Ashley Barnes was sent off for a late second booking.
The point kept Burnley 10 clear of the drop zone, and lifted them to 11th in the table.
Dyche said: "We created enough, I was pleased with the chances we created and the mentality to take the game on, because there's a lot of positive noise about Hull at the minute.
"We weren't sure how that would pan out because it's different playing us than playing Arsenal, because everyone sees that as a free one, and there's more on it against us.
"The only thing I'd question from our point, and I said this to the players, was just that top third moment. We got into some brilliant positions, but there was an overhit pass, an overhit pass, but generally I thought we gave a good account of ourselves."
Burnley started the first and second halves well, but couldn't get their noses in front: "I thought we started both halves ever so well. They had a good middle spell, and then they scored, and we reacted well, as we always do.
"It was a tight game but I'm really pleased with the mentality of the players, because a lot is made of our away record, and there's no fear there.
"We were more than ready to take on the challenge, and it bodes well for the future, but we have to keep doing it. Keep stepping on and playing on the front foot."
The point was a valuable one in the scheme of things as well: "Every point is a good point, particularly away from home, every manager in the Premier League will tell you nicking points away from home is a really important part of it.
"All the noise from last week goes away immediately as well, a different team today that looked like a different team."
Dyche felt the penalty was tough on his side, but sympathised with referee Martin Atkinson: "The penalty is a harsh one all round. It's hard for the referee. From where I was, 50 yards away, there seemed to be a melee, and I thought he'd done well to pull an arm out of that.
"When I saw it back, Keane goes with his head and a natural position is to put your arm up there. Maguire pushes his arm onto the ball, not deliberately, but he hasn't thrown his arm to handball it, he's gone to head it.
"How do you define that for a referee? It's easier on a screen afterwards.
"I'll not make a song and dance about it because it's a tough one to call.
"You've seen them not given, and seen them given."
However, he was aggrieved with Barnes' dismissal, which rules him out of the trip to Swansea: "Barnesy's second booking is a booking, but the first one...the behaviour of our players is immaculate.
"He said he'd ran a bit, and I said 'he's not the quickest', so I don't know how aggressive he was, but it didn't look aggressive to me.
"And he's said no expletives, just pointed to say their lad has pushed Keano into it. I think that's harsh to get a booking for that."