The young midfielder was also full of praise for the club's new signings and their impressive debuts.
The Hammers were handed a tough opening fixture with a visit to the Emirates for their opening game of the new season, with few expecting them to leave their rivals with all three points.
However they did just that, with them coupling a solid defensive play with some excellent counter attacking football to eventually run out 2-0 winners courtesy of goals from Cheikhou Kouyate and Mauro Zarate.
It was the ideal start for manager Slaven Bilic, and Poyet says it was built on a perfect game plan.
“We all know how hard it is to play away at Arsenal. Not many teams get a result there,” he wrote on Kicca.
“You know they are going to get a lot of the ball but we went to The Emirates with a game plan and as everyone can see it worked really well. The game plan was perfect.”
Impressive display from new signings
The young midfielder was also full of praise for the club’s new signings and the performance they all put in in their first Premier League games.
Bilic has brought in a number of new faces this summer as he looks to revamp his squad and have them playing a better brand of football, with signings such as Dimitri Payet likely to be key to that aim.
The Frenchman enjoyed an impressive debut at the Emirates as well, while defender Angelo Ogbonna was also solid at the back, and Poyet says it was one of the best performance from them in a couple of years.
“The new players did well seeing as it was their first Premier League game,” he added.
“All of them stepped up to the mark and more than impressed. It was one of the best performances I‘ve seen from us in a couple of years.”