The result means that the Welsh side remain rock bottom of the Premier League table but are now just four points from safety, and Carvalhal was quick to point out that they are now unbeaten in their last two away league games.
"I'm very happy, two away games and we get four points – it's not excellent but it is good," he told Match of the Day. "Against Tottenham [at home] we had no points but we played well and deserve more. This game we prepared really well to play with the ball, I think we had 57% possession but we also tried to move the ball into the spaces to create damage to the defensive organisation of Newcastle.
"When we arrived, I believe no one outside Swansea believed we can stay in the Premier League but I believe when we achieve a draw here, playing good football against a good team I think people will look and see these guys are reacting. It's our challenge, we are achieving points in a difficult situation, but we are reacting."
Carvalhal's side next welcome Championship leaders Wolverhampton Wanderers on Wednesday night for an FA Cup replay before welcoming Liverpool in the league on January 22.