JJ capped a fine individual display by grabbing the opening goal in the 37th minute, just reward for a dominant spell towards the end of the first half.
We stayed in control in the second half and Arsenal had barely threatened but broke through in the 79th minute when Theo Walcott raced after Eduardo's pass, was met by Young-Pyo Lee in the box and his shot flicked up off his hand and home.
It leaves the semi-final finely poised and the winner will take all when we met at the Lane for a place in the final at Wembley.
"On the whole it was a good performance," reflected JJ. "Arsenal are a good passing side but we managed to press them in the right areas, got amongst them and created chances because of that.
"I think frustration is the word. There is another game to be played and that's what we'll focus on. We had the chances to maybe put the tie to bed but it's difficult to say that when you play against a team like Arsenal because they are always likely to score goals.
"There are positives to take out of it but we always knew the tie was over 180 minutes, two legs and we have to stay focused, get the result and get to the final."
Chelsea complete a high-profile couple of games when we return to league action at Stamford Bridge on Saturday. "We're looking forward to these games, not going into them worried at all, we're excited by them," added JJ.
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Jermaine Jenas couldn't hide his disappointment at not beating Arsenal in the Carling Cup on Wednesday night but insisted the focus had to be on the second leg at the Lane.