Branthwaite, who made his season debut last weekend after undergoing groin surgery in the summer, suffered a thigh injury during training this week.
Mykolenko, meanwhile, suffered a muscle strain during Everton’s 2-1 win over Crystal Palace last Saturday and has been unable to recover in time for Newcastle’s visit to Goodison Park.
‘It’s been frustrating from pre-season until now,’ Dyche said before kick off.
‘You know, every time we take a step forward with the injury side of things, unfortunately we get another injury and then two or three at a time. So it’s been very difficult up until now. It remains difficult losing two players and two very good players.’
When asked how close Mykolenko and Branthwaite were to starting the game, Dyche said: ‘It was unfortunate, Myko took a knock last weekend.
‘We thought it was a knock, it settled down and then turns out to be a small strain and it’s too much for today.
‘Jarrad is similar, just a minor strain but it’s just come too quickly for the game.
‘We know he had a period out and we were hopeful to get this game out of the way, for him I mean, and then obviously he’s got a couple of weeks to sort of get your body to balance out but that hasn’t happened.
‘We’re confident with the injuries going forwards but not enough for today. What it means is an opportunity for others and it’s an opportunity for players to come into a side that has at this moment got a bit of momentum.’
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