The Cardinals' 27-13 win Sunday at CenturyLink Field in Seattle severely hurt the Seahawks' chances of getting a first-round bye in the NFC playoffs.
"I'm just a piece of the puzzle in this great cog we have going," Drake told reporters.
Arizona (5-9-1) out-gained Seattle 412 to 224 in total yards and sacked Seahawks quarterback Russell Wilson five times in the win. The Cardinals also won despite losing quarterback Kyler Murray to a hamstring injury midway through the third quarter.
The Seahawks (11-4) also lost star running back Chris Carson for the season, due to a hip injury he sustained in the second quarter of the loss.
Cardinals pass-rusher Chandler Jones had four sacks in the victory.
"Unfortunately, we aren't playing for the playoffs, but ... we want the success from now to roll into next season," said Jones, who leads the with 19 sacks this season.
Seahawks quarterback Russell Wilson threw a three-yard touchdown pass to Nick Bellore to give Seattle a 7-0 lead with 8:50 remaining in the first quarter.
The Cardinals answered on the next drive, when Drake broke loose for an 80-yard rushing score. Drake's touchdown sprint began a run of 20 unanswered points for the Cardinals, propelling the victory.
Murray connected with veteran wide receiver Larry Fitzgerald for a 21-yard score 4:16 before halftime. Cardinals kicker Zane Gonzalez connected on a 22-yard attempt just before the break, giving Arizona a 17-7 halftime lead.
Gonzalez hit another field goal on the Cardinals' first possession of the second half. Seahawks kicker Jason Myers made two four-quarter field goals for Seattle's only points of the second half.
Drake ended a nine-play, 78-yard fourth-quarter Cardinals drive with a three-yard rushing score, increasing Arizona's lead to 14 points down the stretch.
Murray completed 11 of 18 passes for 118 yards and a score, while rushing for 40 yards, before his departure. Brett Hundley completed 4 of 9 passes for 49 yards in relief of Murray.
Wilson completed 16 of 31 passes for 169 yards and a score in the loss. The Seahawks will need help at running back in the postseason. Seattle also lost Carson's backup, C.J. Prosise, due to a broken arm he sustained in the second quarter.
"We had a really difficult day, obviously," Seahawks coach Pete Carroll said. "Boy, nothing worked out the way we wanted it to, other than the first couple of drives. After that, we just weren't able to do enough to have a chance to win the game.
"It didn't matter what phase we were in. We just weren't good enough."
The Seahawks end the regular season with an NFC West matchup against the division-leading San Francisco 49ers at 7:20 p.m. EST Sunday in Seattle. The Cardinals face the Los Angeles Rams at 3:25 p.m. Sunday in Los Angeles.