The Blades lost out on the second automatic promotion spot to Sheffield Wednesday on the final day, but finished nine points ahead of fourth-placed Huddersfield and 17 better off than play-off semi-final opponents Stevenage.
"We got 90 points and scored an awful lot of goals, but unfortunately that wasn't enough and now we face Stevenage," Simonsen told the club's official website.
"We believe we're the best team in the play-offs and the league table reflects that, but only we can make sure the best team gets promoted at Wembley."
He added: "We said that we would be willing to fight through the play-offs and it's good that we have had this to fall back on.
"Because of missing out on automatic promotion, having led for so long, means we are doubly determined to be successful via the play-offs."