The Saints' blend of home-grown talent, long-serving players and big-money additions has seen them enjoy a fine second season back in the Barclays Premier League.
Their players publicly spoke of their European ambitions earlier in the season - talk which gained credence when they moved within a victory of topping the table in November.
Mauricio Pochettino's side have tailed off since then but are looking to end the season strongly and can move back into eighth with victory against Newcastle on Saturday - a minimum requirement for frontman Lambert.
"We aimed for fourth this season and people laughed at us, but they didn't laugh at us straight away when we were second, they waited until we dropped off a bit," he told www.saintsfc.co.uk.
"Our desire is to get into the top four and that's the way the club has been run in the past four years and that's the vision the players have and it's the one the club has, so for me it's what the players still want going forward and it's what we're expecting to be honest.
"We definitely believe that we can finish above teams like Newcastle.
"I think we adapted to the Premier League last year so we stopped thinking about things in terms of what clubs are bigger than us.
"We're Southampton, we get on with our own stuff, and really you're only as big a club as you want to be in your own head, so if you want to think you won't be bigger than Newcastle then you never will be, but it's up to us to push on."
- Sports & Recreation
- Barclays Premier League