England won 3-1 in Helsinski thanks to goals from Jack Grealish, Trent Alexander-Arnold and Declan Rice.
Afterwards, questions centred on Carsley's position and his chances of landing the fulltime job.
He said, "I keep saying the same thing. My remit was six games and I'm happy with that.
"This is a privileged position. Really enjoying it but I didn't enjoy the last two days. I'm not used to losing in an England team, I don't take losing well.
"People are always going to try and put their chips on one side. I'm in the middle. My bosses have made it clear what they need from me.
"This job deserves a world-class coach that has won trophies and I am still on the path to that."
Carsley was also asked if he is out of the running for the post.
"Definitely not," he said.
"The point I was trying to make is that it is one of the top jobs in the world. I'm not part of the process but it deserves a top coach. The players we have available, we've got a real chance of winning. That was the point I was making.
"It was the fact that this is a world-class job. This will be up there with the best jobs in football.
“Whoever gets it is going to be at a high level. It is a privilege to do this job and I feel really well trusted.
"That's why it was so tough the other night to lose the game and have a defeat. The response has been good."