The city has underestimated both the scope of its bedbug problem in schools and the response needed to deal with it, say critics who have followed the parasitic pests’ resurgence in recent years.

More than 3,500 cases of bedbugs were confirmed in an untold number of schools last year, but city officials said just one school was actually infested. Now, the city is on the verge of finalizing long-awaited contracts with three pest control companies — but the contracts don’t reflect last year’s spike in bedbug cases, and critics say they are inadequate to deal with the problem.

Department of Education officials have long maintained that schools aren’t hospitable environments for the nocturnal insects, but one pest control executive who has done business with the city says they aren’t looking hard enough.

“I don’t think they’re serious about the problem,” said the executive, who asked to remain anonymous. “They don’t want to know there’s a problem. They don’t want to spend money on the problem.”

He said his company didn’t try for the new contracts because he thought the contracts were “woefully underbudget” to deal with the problem. In fact, he said, the costs associated with the task would put have put his company at a loss.

Two of the contracts are worth $14,999 and estimated 225 hours of work for each pest management company — an hourly rate of $67 — according to price quotes that the DOE published when it began collecting bids from vendors.

The contracts have gone unfilled for nearly a year after the previous contract, a three-year, $99,999 deal, was terminated because exterminators treated a school improperly.

The third contract doesn’t specify a price, but estimates 2280 hours of work would be needed. At the same hourly rate as the two smaller contracts, the total budget for bedbugs this year would still be under $200,000.

“I think it’s way too low,” said City Councilwoman Gale Brewer, whose legislation in the council led to the creation of a bedbug task force in 2009. “I hear from people all the time who have had bedbugs and it costs them $400 per room.”

The isolated infestation, at P.S. 70 in Queens, was revealed in response to Brewer’s letter in July pressing the Department of Education to disclose which schools had bedbugs last year. The letter was prompted by a report on GothamSchools that reported a threefold increase in bedbug cases.

P.S. 70 parents and its own principal weren’t notified of the infestation when it happened, according to a Daily News report. It’s at least the second time the school has dealt with bedbugs, too. P.S. 70 was one of the first schools to report the discovery of bedbugs in 2006, the year the city began keeping track, according to a report in the New York Post that year.

DOE officials define an infestation as showing “evidence of breeding” and they say most of the instances involve “one or two” bugs.

Detecting that evidence is difficult. The best way is by using bedbug-sniffing dogs, but two of the contracts don’t require the service and the third requires it minimally because, according to the contract’s language, the DOE “does not anticipate high usage.”