The full-back was thankful for the win against Elche in a difficult encounter, while the Welshman played the modesty card after his thunderous strike
The plucky visitors resisted but los Blancos ultimately claimed the points thanks to Bale's wonder strike from outside the box, flanked by goals from Asier Illarramendi and Isco.
And Carvajal was full of praise for the Wales international and feels the result bodes well ahead of his side's Champions League date with Schalke this week.
"I was ahead of Bale [when he shot]," the defender told reporters. "There was so much sound as the ball passed overhead. It was certainly an amazing goal.
"This result, another 3-0, gives us confidence. It will be a difficult game on Wednesday. We will give our all. We won't think about the league or the derby [with Atletico Madrid] yet, just Schalke."
Bale was satisfied with his goal but insisted what really counted was taking the capital side a step closer to their objectives.
"The most important thing's the three points. It was a difficult game and we had to work for it, but I am happy to have gotten a good goal," added the Wales international.
"We want to win every game in every competition and tonight we had to win to put pressure on our opponents."
Carlo Ancelotti's men now sit three points ahead of title rivals Barcelona after the Catalans suffered a 3-1 defeat at Real Sociedad later on Saturday.