Adrian produced a fine performance in West Ham's 1-0 defeat to Werder Bremen on Friday, and the Spanish goalkeeper feels he could have done "nothing more" to prevent the loss.
It was the first of two friendlies that the Hammers played against the Bundesliga club - with Adrian being given the whole 90 minutes to stake his claim for a regular starting berth.
Joe Hart was then given the nod for the second match on Saturday following on from his loan move from Manchester City.
It is widely believed that the England international will start the season as first-choice, but Adrian produced a string of saves - especially one double stop in the second period - which will give manager Slaven Bilic something to ponder.
"I will always try to help my teammates with saves when I play and to keep the game open," Adrian told the club's official website.
"But, at the end of the day, we lost the game and we are not happy with that result. Personally, with my performance, I could do nothing more.
"The goal was so quick, a quick ball to the striker and he passed it into the corner of the net via the goal post, so I had no chance.
"Then we had a good chance before the end of the first half to draw level at one-one with Pedro Obiang.
"In the second half, we played with more tempo and intensity but at the end of the day we had no clear chances to score a goal in the second half and we needed to be a bit more clinical."
When asked about the arrival of Hart, the former Betis player seemed to welcome the competition he will bring.
"Joe is a great ‘keeper and is an international for England he brings great competition," he added.
"He is a great worker and, like everyone, we are both training very well.
"We have a lot of competition in goal this season, so I will try to give my best and we will see the manager’s decision."
