Venables said: "What are people trying to do to Frank? What are these personal feelings all about? The whole country wants us in those finals but booing one of our own players like that is hardly going to help.
"Were they Estonian supporters in disguise? Don't they realise they are upsetting the whole situation? Frank's last three full games for England have been as good as any player yet he's still getting stick.
"It's really ugly and it's got to stop.
"To me, Frank has shown a lot of guts in dealing with it. I don't know if it concerns him but it's made him into a stronger character.
"We had an amazing crowd on Saturday of nearly 87,000 and there's about 1,000 letting everybody down.
"It's absolutely appalling and must not carry on to big nights like we have in Russia on Wednesday.
"It happened to David Bentley and Phil Neville but no one seems to get it quite as much as Frank.
"These so-called fans are making the game easier for all our rivals."