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Slegers described an "unbelievable performance" in the second leg because of the fightback Arsenal knew Chelsea would give.
Goalkeeper Daphne van Domselaar returned to the starting XI and put in a stunning performance, denying Sam Kerr on several occasions in the second half.
England defender Lotte Wubben-Moy was a rock at the back in the absence of Leah Williamson and Arsenal were not shaken when fellow centre-half Steph Catley went off with a calf injury at the end of the first half.
In-form striker Alessia Russo was full of tricks and flicks. The England international usually keeps touches on the ball to a minimum but she did what it took to escape tricky situations when pressure was building.
Slegers said her team were prepared to "suffer" in order to get what they wanted and it paid off in the end.
"It's suffering for something you love. I think that's what the team did really well. They were prepared for a difficult scenario and for momentum shifts," she added.
"In the first 15 minutes, potentially at the end of the game when things changed again, they just stayed in the 'controlled middle', as we call it.
"They stayed in the game and were constantly in control of whatever scenario or momentum swing. They did their job. Mentally we were in control.
"Of course, we wanted to stop them getting chances and in an ideal world there are no shots but it was two really good teams going against each other."
Former England captain Steph Houghton said Arsenal were "better in big moments" and deserved to progress on the balance of the tie.
Brighton forward Fran Kirby added: "Arsenal allowed Chelsea to have the ball, they were comfortable in their block and defensively worked really hard.
"With the opportunities that they had, they could even have gone on and won the game, so they will be really proud of the performance.
"It showed a different side to Arsenal. It showed what they can do when they have to defend."
Arsenal will hope to book their place in the final when they take on the winner between Lyon and Wolfsburg - who play each other on Thursday night.
The final takes place on 23 May in Oslo, Norway.
