Everton nearly snatched a victor when Seamus Coleman struck the crossbar 15 minutes from time, but it is now only one victory in eight games for the Toffees.
However, Carvalhal had Lukasz Fabianski to thank for keeping his team in the game.
While many of Swansea's fans would have hoped for much more from their visit to troubled West Brom last weekend, a draw was not necessarily a bad result.
40% of Swansea home games this season have had less than 1.5 goals so in light of that, getting paid out at 2/1 on it happening again looks a decent shout.
In Jordan's absence, Swansea struggled for goals, having scored just once in the three games played.
"Things can be completely different from one week to the other just because of the emotions on the table".
"Even though we are moving slowly, it is a positive, and if we keep on playing like this we will make everyone happy".
Free Cavaliers shirt for anyone attending Game 1 or 2 vs. Pacers
Cleveland swept Toronto in last year's playoffs, and they defeated the Raptors in two games toward the end of this season. Green was 0-for-7 from the field, 0-for-3 from the line and the Cavs were outscored by 15 when he was on the floor.
Although wins for rivals Crystal Palace and Huddersfield dropped them two places to 17th, Swansea now have a five-point cushion above the relegation zone.
With fixtures against Manchester City and Chelsea still to come, Carvalhal showed his awareness of how key success could be against Everton.
Opta tell us that Everton haven't won here in their last three attempts and though the Toffees did win their last away game - at Stoke- you'd have to go back to mid-December for their previous away win on the road prior to that.
"We are sure that fans of Swansea, like they have so far, will be part of the game".
Responding to the supporters' reaction, Allardyce added: "I never get annoyed by the fans (reaction), but you need to give some credit to the opposition".
I'm taking over from Mr. Hives until the end of the season, as the guy has taken a much needed early holiday.