Abraham missed the decisive penalty in the shootout to give Liverpool victory in Istanbul last month and was then subjected to abuse on social media.
“I remember speaking to my mum, she was emotional, she was in tears,” 21-year-old Abraham told CNN.
A Chelsea spokesman said the club was “disgusted” with the “abhorrent” posts.
In August, Liverpool goalkeeper Adrian kept out Abraham’s spot-kick to secure a 5-4 shootout victory for the Champions League winners after it had finished 2-2 after extra-time.
Abraham, who has since scored four times in Chelsea’s past two matches, added: “It’s obviously not nice, seeing your son getting abused. My mum was just thinking, ‘Why him?’
“For me, I am a strong character, it doesn’t affect me as much, but it could affect people who don’t have my personality.
“I was sat in the changing room straight after the game and went on my phone. I wasn’t going to shy away from the situation, although I did have some supportive messages. The other side is not nice to hear.
“I went through a lot of emotion after the penalty miss. I had experience of taking penalties last season, big ones as well. Everyone misses penalties. To miss the penalty… I was devastated and I had a lot of abuse after.”
Abraham, who has made two international appearances for England, praised the support he has received from his club, his team-mates and his manager.
“Frank Lampard always had his arm around my shoulder lifting me up, the boys as well, it was like I never missed with the way they supported me and lifted me up – that is exactly what I needed,” added Abraham.