Chico, who has shone for the Swans since joining from Genoa last summer, ruptured ankle ligaments against Queens Park Rangers on Saturday and had to be stretchered from the field.
It is unclear how long he will be sidelined for, but he is expected to sit out at least the Premier League clash with Liverpool on Sunday and the Capital One Cup final against Bradford on 24 February.
"We spoke to him at half-time and he didn't look very happy," Rangel told the South Wales Evening Post on his fellow Spaniard.
"He's been a very important player for us. He's been a rock at the back with Ashley Williams and he will be a big miss.
"We know we have other players who can fill in and do well. But I am very sad for him because he's had an amazing season. Hopefully this won't be too serious.
"I am sure if it's not anything serious like a broken bone or ligaments he's going to try to rush back for Wembley.
"It's one of the finals you've been dreaming of all your life and he knows that. He wants to win a trophy because he's never won one."
Swansea are currently taking in some warm weather training in Dubai and Rangel is confident they can pick up where they left off when they return to Premier League competition at Anfield.
"It's good to go away with 37 points," he added.
"We're not safe yet, but it gives us that extra belief and confidence.
"We've got a great history against Liverpool, we haven't lost to them in the last two seasons. We'll go there and try to keep it the same way."
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