Ivan Rakitic scored the only goal of the game as Barca moved 12 points clear of Madrid in La Liga just three days after knocking them out of the Copa del Rey.
Ramos avoided punishment but Pique felt the Madrid defender's movement was deliberate and that he should have been sent off.
As Pique left the pitch at the break, the Barca centre-back made a talking gesture with his hands to the home fans, implying that they complain about match officials and VAR a lot but many decisions actually go in their favour.
- Real Madrid Player Ratings: Ramos lucky to escape red in 4/10 showing
- Barcelona Player Ratings: Rakitic, Pique give Barcelona backbone in Clasico win
"Leo had blood on his lip," Pique told reporters. "It was aggressive [from Ramos] and it seemed like a red card to me.
"With the gesture, I was referring to the fact they talk [about referees and VAR] but sometimes things go in their favour.
"Pulses are racing at 1,000 miles an hour and it was just a general gesture. I don't regret it, it was how I felt at that moment. I like it when the atmosphere heats up and [the gesture] was to get it going a little bit more."
Barcelona, for the first time in 87 years, now have the edge over Madrid in Clasico history. The Catalans have won 96 of the meetings between the two sides, while Madrid have won 95. There have been 51 draws.
Barca have enjoyed particular success at the Bernabeu recently. As well as winning twice there in the last week, they have now won their last three trips to face Madrid and have won 12 of the last 22 Clasicos at the Bernabeu.
"The results show that we feel good when we come here," Pique added. "I love coming here. This is why I'm a professional, to play games like this in this atmosphere. It can be difficult to motivate yourself for other games."
Barca's latest win moved them 10 points clear of second-placed Atletico, who play on Sunday, but Pique said it would be a mistake to think a fourth league title in five years is already wrapped up.
"We've made a statement [beating Madrid] but it's not definitive by any means," he said. "It allows us a certain amount of calm for the final games of the season but it won't mean anything if we mess up against Rayo Vallecano next week.
"It looks good but last season we were in the same situation. We hope to do better in the Champions League, because we won the other two [La Liga and Copa del Rey] last year. What happened last season is a lesson."