The Hammers lost a third successive Premier League match as fans protested on and off the pitch about the club's ownership, with captain Mark Noble clashing with one pitch invader during the game.
Lampard, speaking on Match of the Day said that the fans have a right to ask questions of the club's board, but lamented their action in doing so on Saturday.
"It was very toxic today, a horrible feeling in the second half," the former England international said. "Fans confronting the players, I understand Mark Noble's position, he's Mr West Ham, he's a fan. This isn't right, whatever way you look at it.
"This was very aggressive today. I understand some of the fans' problem, they lost an identity moving stadium.
"The club have a £29m net spend since they've moved. It's not enough, they've gone backwards. So fans are asking the question - but not mid-game."
West Ham, who are three points clear of the relegation zone, have three weeks to prepare for their next outing against Southampton.