After the match, Grayson claimed three of his players had been punched on the pitch with the Yorkshire club alleging on-loan defender Shane Lowry, Robert Snodgrass and one other player were struck.
He criticised Cumbria police, who arrested 10 fans during the disturbance, telling BBC Leeds: "The police have done nothing about getting our players off quicker or protecting them.
"The stewards have done nothing about it and that's a serious issue for me.
"I'll be taking this further with people involved at a higher level. I'm going to make my feelings well and truly known to the people that matter."
Chief Inspector Mark Pannone, who led the policing operation at the match, said the situation was dealt with "swiftly and robustly".
He said: "We are disappointed by Mr Grayson's comments.
"The policing and the stewarding of the match was conducted in a restrained and professional manner.
"The job of the police is to support the stewards, to prevent disorder and respond to incidents as they occur, which is exactly what we did.
"As soon as the pitch invasion commenced we began working with the stewards to clear the pitch and protect the away fans."
He said the force has not received a formal complaint from Leeds, but the Yorkshire club have said they intend to lodge a complaint with the Football League.
Leeds chief executive Shaun Harvey said: "It is our current intention to make a formal complaint to the football authorities about the apparent lack of security arrangements in relation to the safety of our players at Carlisle.
"It is also our intention to supplement the evidence we already have by having further conversations with both Carlisle United Football Club and the Cumbria Police Force."
Harvey added: "We'd like to offer our congratulations to Carlisle United on reaching the final of the Johnstone's Paint Trophy and we will turn our attentions on the field to our remaining 18 league games and our quest for promotion."
Grayson added: "I'm still very unhappy at the lack of protection afforded to my players and I'm pleased that the club will be taking the matter further with the relevant authorities."
Carlisle's managing director John Nixon said the situation was dealt with "in text-book fashion" and that stewards and police officers worked together to bring the pitch invasion under control "as quickly as possible".
But Harvey countered: "Our players found themselves in danger which isn't what you want to see.
"I have spoken to Simon (Grayson) this morning and on reflection he feels the same way as he did last night - that his players were put at risk.
"We will be contacting the FA to make the complaint, and we have spoken to Carlisle and the Cumbrian Police on the basis that we're going to make the complaint. We will make that and it'll be up to the FA to address that.
"What we hope to achieve is a review of the arrangements that were in place, that ultimately people learn a lesson from what happened, that a group of players are never subject to that again and if any lessons can be learned on a wider scale."
Harvey added: "It wasn't textbook in our view. It certainly wasn't the same textbook we would have used.
"They certainly succeeded in keeping the two sets of supporters apart, which I firmly believe was the priority for them.
"What they haven't done is protect the safety of our players, so if the roles had been reversed I would have stopped short of saying it was a textbook approach, although they are entitled to their view as we are to ours."
Leeds have also questioned the decision to stage the penalty shootout in front of the Carlisle fans instead of at the neutral end.
Harvey added: "How someone can justify that it's not safe to take them in front of an open terrace with no supporters is a question I'm glad I don't have to answer."