The Paris Saint-Germain superstar was fouled 10 times as Brazil drew their opener 1-1 against Switzerland, the most at a World Cup since Alan Shearer against Tunisia in 1998.
A pre-tournament friendly against Austria brought similarly robust treatment for Neymar, who limped out of a training session earlier this week, with Selecao boss Tite admitting the 26-year-old has rushed ahead in his rehabilitation from a broken metatarsal sustained at the end of February.
There was no shortage of tough tackling on display as Costa Rica lost 1-0 to Serbia in their first group outing, but Ramirez told a pre-match news conference at St Petersburg's Krestovsky Stadium his players will not resort to illegality with their place at Russia 2018 on the line.
"Neymar is a very skilled player and it is true we have seen how people have tried to stop him a little aggressively," he said.
"We have our own strategy and we'll see what happens. We'll see – maybe we'll cover him with two men – we'll see. But, of course, we do not want to see any unfair attacks against him.
"My players know what to do."
Of greater concern to Costa Rica supporters this week were reports of a breakdown in relations among factions of their squad, most notably between Real Madrid goalkeeper Keylor Navas and other senior players.
Ramirez took the opportunity to strongly dismiss the allegations when they were brought up.
"In this case, certain information has been published. Supposedly it comes from inside the team but I wouldn't say so," he said.
"It's true that some players are closer to some than others but there are no different groups. There are no problems within the team and I have not had to intervene at all. There were no clashes.
"People have talked about bets between the players but I have not had to stop any clashes.
"I cannot believe it has happened because they are all very polite people. Whoever is sharing this information is not acting correctly.
"If someone is feeling badly personally then they should come to me and I will take the correct decision. But I haven't seen anything."