The 27-year-old, who joined from Real Betis last summer, has recently dislodged Jussi Jaaskelainen as the Hammers' first choice following a string of fine displays.
Adrian starred in the recent 2-0 wins against Norwich City and Aston Villa, while he claimed the Man of the Match award after successfully shutting out Chelsea in last month's 0-0 draw at Stamford Bridge.
Sam Allardyce's side have the most clean sheets in the Premier League and Adrian is optimistic of holding onto that record on the back of their recent form.
"It's only my job! It's my job to stop everything and Tuesday was a great day, because that's another clean sheet," he told West Ham's official website.
"Four in a row is really, really difficult in the Premier League and I am really happy. We have to keep going in this direction.
"As a goalkeeper, when you have confidence, confidence in the manager and in the other players, you are happy on the pitch.
"Sometimes I have to help my team-mates and other times, not too much, but on Tuesday I made three or four saves to help the team.
"It's really, really amazing. The clean sheets are important for the team and it's even more important for me, because I'm the goalkeeper.
"I work every day with Marge [Martyn Margetson, goalkeeping coach], Jussi [Jaaskelainen], with Rafa [Raphael Spiegel], with Hendo [Stephen Henderson] on the training ground for that and this is my job."