The Owls booked their play-off place with a 3-0 win against Cardiff on Saturday.
With one game left of the regular Championship season the Owls know they can only finish sixth, and a play-off semi-final date with either Middlesbrough or Brighton & Hove Albion beckons.
Carvalhal's men are 14 points worse off than both teams currently battling for second place but until a five-game winless streak during February and March, the Portuguese was hopeful of catching them.
"We were near the first two positions, I think six or seven points in one moment," the 50-year-old told the Sheffield Star.
"I had a wish in the moment we could go for the top two positions."
Surprise defeats to Preston North End and Rotherham United followed for Wednesday, who also drew to Queens Park Rangers and promotion rivals Hull City and Brighton during the same five-game spell.
Carvalhal has no doubt what was to blame for the Owls' sudden loss of form.
He added: "But I don’t need to remember what happened in four or five games.
"We missed players, we did not have luck with the decisions of the referees."
Top scorer Fernando Forestieri was the Owls' biggest loss throughout that period, having sat out three games through suspension.
The Italian forward was controversially dismissed in consecutive fixtures for two bookable offences, having been adjudged to have dived for two of them.