Injuries and illness impacted the Toffees’ team selection which Dyche said made the game awkward from the start.
“We put together the side this morning, we had one morning’s work with them, and of course, you can only do so much work when you have a game. Three players came in ill, so that changed the thinking. We’ve had a couple of injuries that we’ve had no chance but to leave out.
“That being considered, the way they’ve gone about the general game – of course, the end product of a win is what we wanted – but the general performance was pleasing for a lot of the players.
“I think they've applied themselves to go and win a football match and create chances. We haven't done that and it ends up on penalties which is not ideal, but that's the way it goes. We practise them, the players did well on the penalties today because it was such short-notice, and they mostly delivered them well.”
Dyche also mentioned his team's inability to kill a game which has been lacking in recent weeks after Aston Villa and Bournemouth both came back to steal three points despite Everton dominating.
The case was the same against Southampton which Dyche feels needs to change.
“Yet again we’ve created golden chances, and you’ve got to score those chances and that changes the whole game,” explained the Everton manager.
“There’s been times we’ve scored goals and looked like we can score goals, but you’ve got to kill games off. If you’re not keeping clean sheets, you have to kill games off and we’ve not done that.
“That’s a nemesis for us. It’s been here a long time, and we’ve tried to correct it and tried to find those moments, but that’s the hardest bit as a manager.
“We’ve got in some amazing positions again tonight, with one on ones, but we haven’t scored a second goal. Obviously, the work continues.”
Harrison Armstrong made his debut for the club whilst 19-year-old Roman Dixon made his second appearance in two excellent performances.
“It was good to get minutes into them and to get them playing here at Goodison,” he added. “Harrison is only 17 – he’s a baby. He’s been out there playing at Goodison Park in a men’s football match, so I’m pleased for him, as well.
“It’s not an easy task. You’re not coming into the team that’s high rolling. They’re coming into a team that’s stretched today and I thought (Harrison) did really, really well to conduct him how he did.
“I think he’s got a very important future and a big future at this football club. It’s early yet. Roman’s done fine, as well, and he gets another performance.
“They’re two definite positives in an awkward night because we wanted to win this game. I made that clear, forgetting the fact we’re down to so few players, we still put out a side there and they put out a performance to try to win.”