"In this moment we are just below it, but we are progressing".
Cenk Tosun headed home his first Everton goal to put the visitors ahead after 20 minutes.
Images showed the forward's exasperation at the display and also going over to angry fans at the end to placate them and no doubt apologise for the performance.
Carvalhal has transformed a side who had earned 12 points from the season's first 18 games under Paul Clement.
Just after the break, with David Moyes' thoughts on being two goals down at half-time presumably still fresh in their minds, West Ham shipped a third. This was very much a performance that had you scratching your head wondering how Swansea found themselves in such a troublesome position.
The New Zealand skipper was stretchered off the field in a neck brace and with breathing support, and also suffered a knee injury in a nasty fall in the 27th minute of his West Ham United team's 4-1 loss away to Swansea City on Sunday (NZ time).
Accusations the players don't care can not be aimed at talisman Marko Arnautovic, though, after cameras caught the Austrian showing he truly cares about the club. "It's easy to play with Marko because he is a good player, he has a good touch, good mentality and he wants to win the games".
'We have trained hard at corners this week, movement, and we scored twice from them.
"Winston has been knocked unconscious and concussed and it's his secondary injury we're more anxious about", he told BBC Sport.
He continued: "We took an important step this afternoon, but life continues and there's still a lot of work to do". We've finally got more points than games played, and we're in 13th place.