Arsenal secured their biggest Premier League away win to move level with Manchester City in second place and two points behind leaders Liverpool.
Saka says Arsenal wanted to make another statement after their 3-1 victory against Liverpool a week earlier.
The 22-year-old winger passed 50 goals for Arsenal with his brace yesterday and is hungry for more as he bids to fire the Gunners to their first title since 2004.
Saka said: "We knew this was a big game and it was really important for us to win and make a statement.
"We did really well scoring six and keeping a clean sheet. Of course, I have my own targets [for how many goals I want to score]. I know these days the media like to compare players.
"I just stay in my own lane and stay focused on what I want to achieve, and what I wanted to achieve at the start of the season. I'm still going and I have got quite a few more to go."
The victory was particularly sweet for Saka as it was at the London Stadium last April that he missed a penalty as the Gunners threw away a two-goal lead to draw 2-2.
That slip-up was the beginning of the end for Arsenal's title charge, however this season they are determined to go all the way and Saka was able to banish the painful memories by slotting in his penalty yesterday.
"If you're going to be a penalty taker, I don't know any penalty taker that scores every single penalty," said Saka (celebrating his second goal, left). "I'm not happy to miss but I understand it's part of the game, so when I won the penalty [yesterday] I was ready to take it again and score.
"I've had many lessons in my career and the best choice is to learn and take the learning process, which makes you stronger."
When you go three or four nil up, it's easy to drop a little bit, but we just wanted more
Arsenal cruised to victory and they were 4-0 up before half-time, with William Saliba, Gabriel and Leandro Trossard adding to Saka's penalty.
Saka grabbed a second after the break and Declan Rice scored a sixth with a brilliant long-range effort, which silenced the West Ham fans who had booed him on his return.
Arsenal's attack has struggled this season, but since the winter break they have scored 16 goals in four games and captain Martin Odegaard believes the team is becoming ruthless.
"I think coming from a big game, a big win, and to come here and back it up with this performance is a brilliant sign," he said. "During the game as well, we just wanted it more and more and I really liked the performance and the mentality of the team.
"We always want to improve, we always want more. I think we showed that during the game as well. When you go three or four nil up, it's easy to drop a little bit, but we just kept on going and wanted more. That's why I really liked."