The 31-year old has recently been a part of the England side, scoring on his international debut against Scotland last month, before adding to that with a goal in the World Cup qualifying win over Moldova on Friday.
Lambert also started in Tuesday's 0-0 draw in Ukraine and although Pochettino is thrilled to see him performing well for his country, he has urged the Saints star to produce more at club level.
"He has played the last two with national side, which must be a huge boost for his self-confidence," Pochettino told Sky Sports 1.
"At the same time strikers need to score goals, that is their bread and butter.
"He hasn't been able to do that, none of them were able to do that, so I'm frustrated.
"We created many chances today and on another day those chances might be goals."