Adrian believes Sunday's defensive performance against Manchester City gives his team plenty of reasons for encouragement ahead of two more fixtures against Premier League high-flyers in the next week.
West Ham follow their narrow loss at Etihad Stadium by taking on Chelsea and Arsenal in back-to-back home fixtures, with Adrian calling for the same solidity they displayed in the north west.
The Spanish keeper was making his first Premier League start of the season, with the on-loan Joe Hart unavailable to face his parent club, and he was thrilled to be able to play his part.
"We made things difficult for City," he said. "We decided to sit back and counter-attack and we did quite well, we had our chances, and we even managed to open the scoring. We knew that in the second half they were going to push much more. They brought all the artillery they had into the pitch.
"In the end their big amount of talent defined the match. Silva scored an amazing goal, we could have made it 2-2 but we lacked a little bit of luck and missed that chance. But we must get something positive even in defeat and, although we are not happy, I think we should continue with the line of defending well and looking dangerous when attacking.
"It was my first Premier League game this season, I try to make it difficult for the coach and give my best and I think I showed that I am still here and I hope to have more minutes from now on.
"It is clear that we have a difficult streak against teams from the top of the table but it is also clear that all Premier League matches are difficult. We have to always play with the same mentality, to get points and go match-by-match."