Leicester boss Brendan Rodgers admits Leicester were priced out of replacing Harry Maguire.
England international Maguire moved to Manchester United on Monday for £80million, a world-record fee for a defender.
PA understands the Foxes did bid around £30million for Burnley's James Tarkowski, but it was swiftly rejected with the two clubs miles apart in their valuations. The Clarets wanted well over £40million.
Leicester also looked at Bournemouth's Nathan Ake - although the Cherries reportedly wanted £75million.
It left Rogers without a replacement and the former Celtic boss said prices were too high.
"Yes, as simple as that," he said. "The club had every right to hold out for what their valuation was for Harry but then everything was going to be very difficult.
"One because of the price and two because that timeline was really tight. We looked at it, it didn't happen, but we're happy with what we have.
"It was always going to be a difficult market if we were interested in one or two other players but the club started to prepare for that a year ago.
"They brought in two outstanding centre-backs in Caglar (Soyuncu) and Filip (Benkovic) and if we weren't to bring anyone else in we know we had them - along with Jonny Evans and Wes Morgan.
"We looked but the market proved too difficult. But we were comfortable with what we had.
"We're very pleased, we targeted a number of areas and delighted with the players we brought in.
"We lost a fantastic player and a really good man. What Harry did over the summer was show how to conduct yourself and also showed good guys get what they want in the end."
Leicester host Wolves in their Premier League opener on Sunday but deadline day signing Dennis Praet is unlikely to feature as he builds fitness while Benkovic continues to recover from an ankle problem.
Meanwhile, Aiyawatt Srivaddhanaprabha was confirmed as Leicester's new chairman on Thursday to succeed his father Vichai, who died in a helicopter crash outside the ground in October.
"He has shown incredible courage, his father lost his life here and the very next day he was here," Rodgers said.
"From that day he assumed the responsibility of leading the club.
"It has felt really natural. He worked very closely with his father in getting to understand how to lead the club and, for me, he has been incredible.
"He has been a focal point."