Olivier Giroud came off the bench to score twice to add to an early goal from Mesut Ozil and Arteta's penalty after Romelu Lukaku scored from close range to briefly peg Arsenal level at the break at Wembley.
Arteta converted from the spot, with his penalty kick having to be retaken following encroachment, to give Arsenal a 2-1 lead after Alex Oxlade-Chamberlain was tripped by Gareth Barry.
It meant the former Everton midfielder ensured he would play at Wembley for the first time after he missed out in the Toffee's final defeat by Chelsea in 2009 due to a knee injury.
"Overall we dominated the game and had the better chances but Everton are a good side and when they broke in the first half they scored a goal. Overall we are happy to be at Wembley," Arteta told ITV1.
Of his penalty, the Spaniard said: "It was a massive moment but I'm happy that I scored.
"It was (a turning point). We knew they had to attack and on the break we would have the chances to score and we took it.
"It would be amazing to (win). We have a good chance. We're in the semi-final at the moment."
Arsenal's most recent silverware came in the FA Cup in 2005.
Everton boss Roberto Martinez agreed that Arsenal's penalty score was the turning point in the game, but he questioned whether it should have been awarded.
"It was the key moment, the second goal. I felt it was a situation where Barry was fighting with Oxlade-Chamberlain for the ball and I felt there was contact but is that contact enough to give a penalty?" Martinez said.
"They are difficult decisions and sometimes you have to be a bit lucky for them to go in your favour.
"It was clear that the second goal was going to completely change the game and that was the case.
"I still feel the penalty was a very soft call but I can see why he made it. It's very important in the final outcome of the game."