Clarets duo are hamstrung
Barnes started the game, but a minute before half-time walked straight down the tunnel at Valley Parade after playing a pass back to Ben Mee and feeling his hamstring.
Jutkiewicz came on in his place for the final minute, but didn't appear for this start of the second half, as he was replaced by Rouwen Hennings.
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Hide AdBurnley won the game 4-1 with two goals from Andre Gray and further efforts from Ben Mee and Michael Kightly.
Boss Sean Dyche explained: "Hopefully it’s not too serious, (Barnes) felt his hamstring a bit tight and a bit sore and he got off immediately.
"I’ve no problem with that, this is no time for heroes, we need fitness, that’s the key thing.
"Juke’s hamstring was tight as well which is why he didn’t come out for the second half.
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Hide Ad"It wasn’t strained or anything but we just can’t afford to take risks at the minute so that’s why those two came off. We have to be careful."
Dyche was pleased with both his players' fitness levels and a powerful display: "It’s about fitness but it’s also about performances, I reminded the players beforehand that as we get deeper into pre-season the fitness gets more natural and we want the performance level to rise.
"I thought there was a good level of both today, physically they looked strong and there was some excellent play, so it was good reminded of what the group is about and what the team will bring to the table."