Mauricio Pochettino's team collected just one win in seven games during December, but the Saints have recovered from their poor run of form and are now unbeaten in their last four matches.
"We've played well now for four games and we've won two and drawn two. I think we were unlucky not to win all of them, to be honest. That is not being over the top," Lambert told reporters.
"I think that was coming, it has been coming for a while and now we have got exactly what we deserved against Fulham. We're confident in ourselves and we always knew that with the run of games we had would make things difficult.
"We got over those run of games with a respectable amount of points and now we have got a run of games which we think we can take a lot of points from. We are more than confident we can do that."
The Saints currently sit in ninth place in the Premier League table.