In the first half at Camp Nou, Varane was caught by a high challenge from compatriot Clement Lenglet and then had his shirt pulled by Ivan Rakitic when competing for a corner.
Referee Alejandro Jose Hernandez Hernandez did not award a penalty and neither incident was checked using the VAR pitchside monitor midweek.
Madrid captain Ramos was left bemused as to why VAR did not intervene, having watched back the footage at half-time.
"We saw them at the break and they look pretty clear. They're both penalties, but we can't change that now," he said to Movistar.
"VAR is here to help. It's bad luck. On another day, it'll be our turn to have a penalty that they don't check."
Gareth Bale saw a second-half goal correctly disallowed for offside after a VAR check, as Madrid failed to make their early dominance count and Barca's front three struggled to get into the game.
The result means defending champions Barca remain top of LaLiga but level on points with Madrid, who are now unbeaten in 12 matches in all competitions.
Ramos, who became the top appearance-maker in the fixture's history as he played Madrid's fierce rivals for the 43rd time, is frustrated the mid-season break starts after Sunday's game against Athletic Bilbao as he wants to sustain momentum.
"You can't be happy when you don't win, but getting something here is always positive," he said.
"We saw a great Real Madrid today, with a lot of personality, on a very tough pitch. We went to steal the ball, which helped us create many chances. There were few mistakes and that's the end result.
"We controlled the game quite well. We had more chances than them. It's not easy to get the ball off them. The strategy of pressing high worked well.
"We're going through a great dynamic in terms of play and we're also good physically. It's a shame the year is ending - we'd like this not to stop.
"Now, we have Athletic and hopefully we'll continue like this after the holidays."