Villa are into the quarterfinals 4-1 on aggregate after winning the second-leg 4-0 via goals from Ollie Watkins, Leon Bailey, Jhon Durn and Moussa Diaby. Sven Mannsverk was sent off for Ajax in the second-half.
Emery said: "We're happy, it was very important. We tried to connect with our supporters. After the first leg we were analysing with the players and we knew before the natch we needed to play better than we did there.
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"The match was a bit slow in the first half. When we scored a second goal and they had a red card it was easier for us."
On Ollie Watkins' injury: "We don't know exactly what the (issue) is. Maybe for Sunday he could be available. Diego Carlos is something with his hamstring. Maybe he might not be available for Sunday.
"It's experience for us. Confidence. Trying to feel strong. We did it here with our supporters."