The Blues have scored five Premier League goals from set-pieces this season, excluding penalties, meaning that 11 clubs have currently outscored them from dead-ball situations.
Past specialists like Willian, Marcos Alonso and Mason Mount have all left west London in recent seasons, as the new owners have produced a near-total overhaul of the squad.
Chelsea have scored four fewer set-piece goals this term than Wolves, whom they face on Sunday, and Pochettino was asked whether a specialist is needed to fix the problem.
"We work a lot on set-pieces," the Argentine told reporters. "We have specialists. We are a coaching staff in charge of everything. We have a group of analysts for set-pieces
"After that, it is about the quality of the player. It is about the takers. We don’t have a specialist. Maybe Chilly [Ben Chilwell] is good in the delivery, but we don’t have a specialist after that.
"If you want to be good in set-pieces, we work a lot. But then you need good takers. When you have good takers, and of course, Wolves have good takers, and like Manchester City have, or other clubs.
"It is not down to the work. We work similarly, but the problem is to have good takers.
"Look before at West Ham, and after. What changed? After and before? It’s not the same. The taker is [James] Ward-Prowse.
"For sure, you can work, like West Ham were working. But now, you add a player like him, you increase the percentage. That is football. Football belongs to the players. Not to the specialists."
Chelsea produced a record-breaking January transfer spend of £323million in 2023 but didn't sign a single player this winter.
Pochettino may have missed Chelsea's big spending boom as new Premier League profit and sustainability legislation slows down the transfer market.
However, it's not an issue for the former Tottenham boss, who believes he must focus on improving his current players.
“I was in Tottenham and didn’t sign anyone for 18 months," he said.
"Maybe it was because we were so good at helping players to evolve. That may be the answer, but we need time to improve the players and perform how we expect to. For me, it was never a problem."