Two Branislav Ivanovic errors saw the Blues surprisingly beaten 2-0 by the Swans at Stamford Bridge in a remarkable smash-and-grab win to leave the Welsh side strong favourites to reach the final.
But the England centre-back insists the tie is not over and has pointed to the example of last season's UEFA Champions League run to show what Chelsea are capable of.
"It is never over. We created enough chances to go in at half-time three-nil or four-nil up," said Cahill, quoted in the Daily Star.
"And if we take those chances in the away leg and keep it tight, we will win.
"It will be difficult because I've certainly found it tough when I've been to Swansea on my last three visits. I got two draws with Chelsea and lost with Bolton, so it is a difficult place to go.
"But we showed we can turn it round when we did it against Napoli in the Champions League last season, so this team can do it - and we need to.
"I think if we had taken our chances we would have won convincingly and there is no doubt we can create chances there."
Negativity
Despite the negativity surrounding interim boss Rafael Benitez, Chelsea went into the game having won eight of their previous 10 matches.
"Normally, we are unbelievably hard to beat at Stamford Bridge and we've been getting results," added Cahill.
"We just have to be consistent in what we are doing.
"Sometimes we are playing fantastic stuff like against Southampton and Everton - but then we chucked it away against QPR and Swansea.
"We're finding it difficult at the moment when teams camp in and put up two blocks of four for us to break down.
"We're having all the possession, but it counts for nothing unless you create a lot. In the first half against Swansea we created chances and if you take one or two they have to come out.
"We were looking to do well so the lads are gutted."
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