Ryan Nelsen believes West Ham have issued a statement of intent by tying Winston Reid to a new deal.
Tottenham are keen for striker Shaquile Coulthirst to continue his development out on loan after his spell at Southend.
The Clarets have signed seven players during the current transfer window, with three of these being free transfers.
And Dyche, 43, says that the spending power of other teams in the Premier League means his side are struggling to bring in the calibre of players he is after to try and extend the club’s top-flight stay beyond this season.
"We are trying (to bring players in),” said Dyche. “A couple of situations are close but a couple have gone away from us.
"People are throwing around a lot more money than us and money makes it work, simple as that. You cannot hide that fact.
"I have got certain financial parameters to work within and it is very difficult on wages and transfer fees.
"In one year the market has gone hugely one step forward and we were already behind the curve because we weren't spending anything.
"We took the club forward so quickly last season. No one was expecting it, including the club.
"Things that you normally put in place weren't in place. That sometimes catches you by surprise, so you have to ramp it up really quickly, and in a market that is running away."
Burnley have parted with fees to bring in strikers Marvin Sordell and Lukas Jutkiewicz, midfielder Michael Kightly and defender Stephen Ward, while also picking up goalkeeper Matt Gilks and midfielders Matthew Taylor and Steven Reid for free.
The Clarets have suffered back-to-back defeats so far in the Premier League this season – to Chelsea and Swansea – and were also knocked out of the Capital One Cup by Championship side Sheffield Wednesday on Tuesday.
Next up for Burnley in the league is a visit from Manchester United this weekend and Dyche is determined not to underestimate their opponents, despite their poor start to the season under Louis van Gaal.
"How could it be even bigger?” he added. “Man Utd coming to Turf Moor.
"We know the challenge in front of us - never more so than when the big guns come to town.
"I don't think you look at them for any other reason than being a fantastic club.
"They have a very good group of players and a renowned manager. We are not naive enough to think they will come here for any other reason than to play hard and try to get a result."Of course, we will do that as well."