The 19-year-old thanked Stoke's Glenn Whelan for his assistance on the pitch, but Shawcross - who left the pitch in tears after being sent off and has sent messages of support to Ramsey in hospital - was not mentioned.
Related ArticlesShawcross: I won't change my styleArsenal v Burnley: match previewWenger: Ramsey injury will not end careerShawcross's 'intent' is not the pointAaron Ramsey faces rocky road to recoverySport on television"I remember what happened clearly and after the tackle went in I saw that my leg was broken and hanging at an angle," Ramsey said.
"I have seen images of the aftermath of the collision again but I don't want to dwell too much on the challenge as I can't change what has happened.
"It is difficult for me to take everything in at the moment. I thought I had been progressing well this season, so of course this is a real setback.
"It is very hard to take but I am young and have time on my side. I had an operation last weekend and, while it will take time for my leg to heal, I am determined and focused on overcoming this injury and hope to be back fitter and stronger than before.
"I have been overwhelmed by the terrific support I have received from so many people, including fans from many different football clubs.
"In particular, I would like to thank the medical team here at Arsenal for their efforts, as well as the staff at both hospitals.
"Glenn Whelan was especially kind and I really appreciated his immediate assistance on the pitch as well as the medical support from Stoke City. I also want to say thanks to Arsenal for helping my family this week.
"Last but certainly not least, I have been blown away by the fantastic messages of support from the Arsenal fans. I am proud to be an Arsenal player and your support has been incredibly touching.
"Finally, I want to wish my team-mates all the best for the remainder of the season. I know that we are capable of winning a trophy and I will be backing them all the way."
Arsenal manager Arsene Wenger initially condemned the challenge as "horrendous and unacceptable", while also criticising Stoke's overall approach.
"I stand by what I said 100%," Wenger said. "I knew exactly what would happen the whole week, that was quite easy to predict.
"I am sitting here like I am in a tribunal. What do I have to defend? Is it a football game or something else?
"I can understand people want to be committed against us, and I have no problem with that.
"I love the commitment of the English game. I don't want to change that and it makes the game even more attractive, but high commitment demands fair intention as well.
"Tackling is an art you do not want to get out of the game. We have some good tacklers in this league, some who are not good, but that does not mean you go into it trying to break a leg.
"It is not Arsenal against the rest of the world. What I say here is valid for the Arsenal players as well.
"I want the Arsenal players to go into the tackles like everybody else, to go into the tackles and be committed.
"What I say it not just for Stoke or Arsenal players, it is for everybody. I defend football. It is not that we are apart from anybody else. We are the same.
"I am continuing to defend the values that I believe are important for our club and football. That doesn't mean we are angels and everyone else is the devil. It is for everybody."
Wenger maintains there is no point in continuing to debate the issue.
"I believe that on our side we have made one decision to support Aaron Ramsey as much as we can and then continue to promote the values that are important for the club and football," he said.
"All the rest is to go into unneeded controversy. I don't see how that can help football or Aaron Ramsey. It is important to focus on the future, help Aaron Ramsey and let people talk."