Alexander-Arnold, having last week announced he would be leaving when his contract expires this summer, was jeered when entering the pitch as a second-half substitute in Sunday's 2-2 draw with Arsenal.
In reaction, Aldridge wrote for the Liverpool Echo: "Everyone is entitled to their own opinion on the decision of a large portion of Liverpool fans to boo Trent Alexander-Arnold when he was brought on against Arsenal.
"Many will differ and everyone connected to the football club, be it fans or former players like myself, will have their own takes on the situation. The first thing to say is I totally understand all that.
"But listening to the noise as a lad from West Derby came on the pitch hurt me. I have been going to Anfield over 60 years and I have never seen or heard anything like that before. I felt sick.
"Us former players, we always stick together, and watching it with the great Ian Callaghan, we felt the same watching on as the boos swept across the stadium every time Trent touched the football. It left me feeling uneasy.
"Liverpool is a family and I respect everyone's views who loves the club but the booing did no good for anyone. All it did was help Arsenal get back into a game they should have had no hope in. The visiting fans will have loved it all, sadly."