With the scores locked 2-2 at the end of extra-time, the qualifying tie went to penalties, with the Czechs eventually winning 3-1.
Eriksen, who was a second-half substitute on the night, spoke to Danish reporters in the mixed zone after the match.
The midfielder said: "It's a scandal that Denmark is not part of the World Cup, yes. I think so.
"The self-examination will go up a proper notch, I think. There will be a lot of blows from the various media, podcasts, and the like.
"There should probably be someone who is after us players because we as a country have not been able to qualify.
"It's deserved and we have to be able to take it - and then we have to rise again. Next time it's the Euros that needs to be achieved and then this will be forgotten."
Eriksen pointingly added: "We have the team to join the final qualifiers (teams). We should have made the qualification given the teams we met. We should also have beaten the Czech Republic."