Reading secured a top-six spot thanks to a nervous 1-0 victory against Wigan, earned thanks to a sixth-minute header from Yann Kermorgant, his 17th goal of the season.
Wigan fought gamely throughout, but missed a series of good chances and were relegated back to League One after just one season in the Championship.
“That level today was not good enough for the play-offs,” Stam said. “We need to step up, we need to do better.
“We’ve haven’t done today what we can do. For what reason, I don’t know.
“Every game in the play-offs is totally different than what it can be in the league and it’s already a big achievement for us that we’re up there.
“There’s no pressure on us. You’ve got to give it your best shot and that’s what we’re going to do.”
Of his players’ nervy showing against Wigan, Stam added: “For us, it was important that we made the play-offs now.
“It was not an easy game and we knew that would be the case. We were playing against a side that were fighting for their lives.
“We started well, aggressively and going forward. But we slowed down after our goal when we needed to keep on going.”
Wigan’s defeat and relegation was marred further by a serious injury to midfielder Shaun MacDonald after a 50-50 first-half challenge with George Evans.
It was confirmed that MacDonald had broken the tibia and fibula in his left leg and would spend the night in a local hospital.
Wigan’s interim manager Graham Barrow said: “I didn’t think there was a lot in the challenge [by Evans]. It was just a tackle, it’s just an unfortunate thing that happened.
“I’m told it [the fracture] did break the skin. It’s probably the third time that I’ve heard that noise, that crack, and I knew he’d broken his leg straight away.”
Barrow added: “At the end of the game, I was disappointed because I wanted to take it to the last weekend. But results went against us elsewhere as well.
“I thought we could stay up, I knew it was a long shot, and I was quite proud of the performance today. But obviously the finishing touch was not there.
“The lads have been great for me but clearly it hasn’t been enough to keep us up.
“There are things we’ll have to look at internally, which haven’t been right, and that’s fact. We are where we are, the table tells no lies.”