Karim Benzema and Gareth Bale converted from the spot in each half, either side of a Roger Marti strike, to move Madrid back to within nine points of league leaders Barcelona.
Benzema opened the scoring after referee Ignacio Iglesias Villanueva penalised Enis Bardhi for blocking a Luka Modric cross with a raised arm, but only after checking the incident on the pitch-side VAR screen.
Villanueva awarded a second penalty after Casemiro went to ground following a wild attempted clearance by Cheick Doukoure, although there appeared to be minimal contact between the players.
Carvajal, though, said he heard Doukoure kick Casemiro and thinks the officials should be trusted to make the right call when VAR is available.
"The first one, at half-time, they told us that he was covering his face. The second, I heard the kick from 25 meters away," said the full-back, as quoted by Marca.
2 - Real Madrid have earned three points or recorded a victory thanks to two goals from penalty spot for the first time at least since 2013/2014 season (in all comps). Decisive pic.twitter.com/V3S62bOW7g— OptaJose (@OptaJose) February 24, 2019
"I'm not a referee; I don't assess the decisions. If both the referee, who was close, and VAR have ratified the penalty decision...
"Other times, we have been hurt and nothing has happened. Being a referee is difficult and we have to keep working independently of that."
Madrid's win keeps their faint title hopes alive ahead of a double-header against Barcelona, first in the second leg of the Copa del Rey semi-final and then in a league meeting next Saturday.
Carvajal admits both games at the Santiago Bernabeu are of huge importance if his side are to keep chasing for trophies.
"Until maths tells us we can't [win the league], we won't say goodbye to it," he added, "For us, the game against Barcelona is a final, but we have the match on Wednesday first."