After a poor first-half display in the 2-1 defeat against a second-string Germany, they turned it around somewhat with a goal from Alex Scott, but ultimately fell short.
Now, they face Spain knowing elimination is on the cards if they do not turn up.
Opta gives England a 35% chance of winning the game in normal time, whilst Spain has a slightly larger 37%.
But, Carsley believes his side feels like they are not the favourites.
Speaking to reporters at England's training base in Samorin, he insisted: "I don't feel like an underdog. I think there's a massive expectancy against Spain and if we can perform and that's all we need to do.
"If we can perform and we can play to our ability, we've got a great chance of winning the game. I believe Spain are a top team and anyone who was with us in the last few Euros knows you have to beat all of the top teams.
"Spain are another team I've got a lot of respect for, the final we had a couple of years ago was so close.
"It could have gone either way. We scored a fortunate goal and played OK in the game, but there's definitely a lot more to come from us if we're going to progress."
Possession-based football will be on show in Trnava on Saturday, with England topping both possession and pass completion statistics. Spain are second in both metrics, meaning whoever controls the ball more in the quarter-final could prevail.
Asked about this, Carsley responded: "It has got to be one of our objectives against Spain, a team that is really possession-based.
"Having all this possession, we've got to finish with an end product. Unfortunately, getting that end product means risking the chance of giving the ball away, which we have to.
"We want our players to play with risk, we have to encourage them to get into areas of the pitch and express themselves."
'Only a matter of time'
Tino Livramento is one of the 'older' heads within the dressing room for England, but, remarkably, this is his first tournament at any age level for the national side.
He missed out through injury two years ago when his teammates went on to win the tournament, and given his age, this could be his last game at age-group football; however, he is not ready to go home just yet.
Speaking ahead of Carsley, the Newcastle United full-back said: "I knew coming into this had to be my last camp for the 21s, so it's a big thing but, again it's just partnered with excitement just to go out there and enjoy the occasion and play as well as I can...
"We've got amazing individuals. I think it's sort of just only a matter of time before the team fully clicks, and tomorrow is just a great opportunity to go out there and do that against a great team like Spain."
Livramento sat out the Germany game after starting the first two group games against the Czech Republic and Slovenia, giving him some time to recover ahead of the weekend's game.
He added: "I definitely feel fresher now, having not played against Germany, but I think when you play at a high level throughout the whole season, I played a lot of games this term, so if Lee wanted to play me he could have played me, he knew that, so I think the main thing is we're into a quarter-final and I'm ready to go.
The full-back has been one of the players linked with Manchester City after starring for the Magpies last campaign, but he is fully focused on the job at hand in Slovakia.
Asked about his future at St James' Park, he replied: "The manager (Newcastle's Eddie Howe), I'm in constant contact with him. He has just said to keep focusing on what you're doing now, and you're doing so well.
"So I think having that relationship with someone that is obviously such a big figure in what I've done so far, I think, is an amazing thing for me."
Follow England's quarter-final against Spain with Flashscore on Saturday.