The South Korea international was caught on the ankle by Chelsea midfielder Ramires during the second leg of their semi-final at the Liberty Stadium.
The former Celtic star concedes he feared he had suffered a serious injury following the challenge, which went unpunished by referee Chris Foy.
Any significant knock would have put his participation in next month's final against Bradford in doubt.
However, the 24-year-old has been given the all-clear by the club's medical staff and he played half an hour of Swansea's clash at Sunderland on Tuesday, much to his relief and delight.
"I was afraid, after the tackle, that I had got a bad injury," said Ki. "I have had a few ankle injuries before, so I know how bad they can be.
"I seriously thought I might miss Wembley when that happens.
"I thought I might not be able to play for two or three months, but I was very lucky."
After seeing his injury fears allayed, Ki admits that thoughts have already started to shift towards Wembley and earning a place in Michael Laudrup's starting line-up.
"We're all fighting for a place in the team at Wembley," he added.
"Every player is ready to play. We have shown this season that anyone can come in and do well.
"We have got good strength in this squad."