Gunners defender Shkodran Mustafi was stretchered off after suffering an ankle injury which may push Arsenal into trying to get a deal done for Flamengo defender Pablo Mari.
Arsenal boss Arteta said: “They were terrific. The courage to play, to make big decisions, to not be scared and play safe. That’s the difference with these three kids. Eddie was terrific and I really like Joe in that position.
“Look at Eddie on the wing and three seconds later there’s a cross and he’s there in the middle. He’s always there in the middle of the goal ready to score. And also the way he works without the ball is terrific.
“A cup run gives you a lift, to go an extra round. You are looking at the next opponent, you are closer to Wembley which is a magnificent day. Let’s go step by step but they are really willing. I experienced it as a player and I want to experience it as a manager now.”
But Arteta did admit that he fears the worst on Mustafi who now joins Calum Chambers, Kieran Tierney and Sead Kolasinac on the casualty list.
Mari travelled to London last weekend but has since returned to Brazil with Flamengo wanting to do a permanent deal for £10m while Arsenal want to loan him until the summer.
Arteta said: “We have a very clear intention of what we want to do in the market with the resources we have. If we can do it, fine. But his fitness won’t change anything.
“We are assessing the injury, it is an ankle injury, but when a central defender has to come off normally it’s not good news.”
Bournemouth boss Eddie Howe was critical of his team’s first half display and admitted harsh words were needed in the dressing room at the break.
Howe said: “We struggled with our duels, did not win enough tackles, the basics really. We left it too late.
“Whatever competition you are in, we want to win. I don’t feel I need to say that I believe that we have enough in this squad. But we showed a reaction in the second half and we will have to carry on showing that.”