The striker believes that Mauricio Pochettino's departure to Tottenham in May signaled a lack of ambition, leading players to leave St. Mary's Stadium this summer.
The England international, along with Adam Lallana and Dejan Lovren, joined Liverpool from the Saints this summer, while Luke Shaw left in a 37 million euro deal to Manchester United and Calum Chambers moved to Arsenal.
Lambert and Lovren made their debuts for Liverpool in Sunday's 2-1 win over Southampton at Anfield and, while the striker received a warm reception from both sets of supporters, the Croatian center back was booed by the traveling fans for forcing through his transfer.
MORE: Coach Ted Lasso returns! | Porter challenges Guardiola | WAGs
Lambert believes that Mauricio Pochettino's departure to Tottenham in May was the catalyst for players deciding to leave Southampton this summer and has questioned the club's ambition under its current ownership.
"[Lovren'll] be okay," Lambert told Fox Sports Australia. "Obviously, a few of the players have took a bit of stick. They'll take it, that's football. It's been surprising that it's all been the players and none on the owners, which I have found a bit surprising.
"There's obviously a reason why the gaffer [Pochettino] went and I think that was the moment that it became clear to the players what the ambition of the club was going to be."
Lambert is grateful for the support that he received from Southampton fans after coming on as a second-half substitute for Liverpool and maintains that he holds a lot of respect for his former club.
"It was good. I love Southampton fans, I've got a good relationship with them, so it was nice that they acknowledged me in the way they did," he said. "I tried to acknowledge them back in the same manner, the same kind of respect. I've got nothing but respect for Southampton, the players and the fans."