Adrian wants West Ham United to follow up victory over Crystal Palace with a win over Southampton on Saturday.
The goalkeeper was in fine form as the Hammers scored a 3-1 Barclays Premier League success at Selhurst Park last weekend.
With the Saints visiting the Boleyn Ground, the No13 is determined to help his team achieve back-to-back wins for the first time since late March, when they defeated Hull City and Sunderland.
"This is a very important match for us because we need to keep the same level of performance which we used to win against Crystal Palace," said Adrian. "In the first game against Tottenham we also made a good performance but were unlucky with the result in the end.
"The last game against Crystal Palace was a very, very hard place to go against a tough team, but we showed very well. We need to keep going at this level and win our first three points at home.
"The Capital One Cup game against Sheffield United was very unlucky, I think, because we played so well and kept the ball and had some chances, but the other goalkeeper performed very well. Penalties are a lottery, because either you win or the other team wins.
"We need to keep getting better, little by little."
Saturday's opponents Southampton have undergone major changes this summer, with a new manager in Ronald Koeman and a host of players leaving and arriving at St Mary's Stadium.
Whoever lines up in red and white stripes, Adrian knows he will not have an easy afternoon against the Saints.
"I don't know if anything is good for us or bad for us, because a lot of players have left and they have a new manager, but the most important thing is us," he continued. "We need to give a good performance and feel comfortable in Upton Park and win the three points. After this game, we have the international break, so it's very important for us.
"Last season Southampton were very strong under Mauricio Pochettino. This season they have a new manager and a new system, but I repeat that we should only focus on what we can do as a team and our own performance, and hopefully we can win."
Adrian has also lined-up alongside a number of new colleagues in the West Ham side this season, including fellow Spanish speakers Mauro Zarate, Diego Poyet and Enner Valencia and Senegal pair Cheikhou Kouyate and Diafra Sakho.
The goalkeeper believes the new boys have strengthened the squad for the 2014/15 campaign.
"I think this season the squad is very competitive because have very good players in every position," he observed. "We have more forwards with Enner, Mauro and Sakho, which gives us very good options in attack. I think Cheikhou and Poyet can also help us."