Smith is set to return from a concussion at Old Trafford when the fourth Test begins on Wednesday, in a huge boost for the tourists with the series locked at 1-1.
The star batsman was ruled out of the third Test, which England incredibly won by one wicket, after being hit by an Archer bouncer at Lord's.
Smith reminded fans Archer was yet to get him out during the Ashes and the England paceman offered a response.
"Well, I can't get him out if he wasn't there," he told UK newspapers, via The Guardian.
"But there'll be more than ample time to get him out. I'm not saying I won't get him out but if we don't get him out there's 10 other people we can get out and if he's stranded on 40 that's not helping his team too much.
"He can't do it all himself. We want to win the game. I'm not here to get caught up in a contest with one man. I want to win the Ashes."
Led by Ben Stokes (135 not out), England incredibly chased down a target of 359 to draw level in the series at Headingley.
Archer believes that win is set to give the hosts a psychological advantage for the remainder of the series.
"That's the thing, never get complacent. To be fair, 359 runs is a lot of runs. The crowd started to get on their backs as well, I think they panicked a bit," he said.
"They probably thought they were going to roll us if they got a few quick early wickets but they didn't and I'm glad we showed some resistance because the series isn't over and in the upcoming games I don't think they'll declare now.
"If they do have a chance I don't think they'll be too attacking. If they draw the series they still get to retain the Ashes."