The former Town forward was an obvious candidate during the penalty shoot-out after the tie had finished 1-1 on aggregate after extra-time.
However, Carvalhal has told BBC Radio Sheffield the 27-year-old 'did not feel confident' as the Owls went on to lose 4-3 on penalties with Sam Hutchinson and Fernando Forestieri seeing efforts saved by Town stopper Danny Ward.
"He said he did not feel confident - the worst thing I could have done was force him to take one," said Carlos Carvalhal.
"It would have been a big mistake to make him take one. It's one of the worst things you can do to a player.
"The five players who took them were the ones who had practised them best and said that they wanted to take them."
Rhodes has endured a miserable time at Hillsborough since making a loan move from Premier League side Middlesbrough in January, only finding the net three times in 20 appearances for the club.
Expected to make the temporary switch permanent this summer for a fee believed to be around £10m, the forward had a penalty saved in Wednesday's 1-0 defeat to Leeds United back in February.