Everton were the only Premier League club not to bring in any players during the January transfer window despite their need to inject life into their squad.
Numerous attempts were made to bring in players on deadline day, the day after Dyche was officially announced as manager, but they were beaten by other clubs or could not get deals over the line.
Despite criticism of their failure in the transfer market - owner Farhad Moshiri gave an interview last week in which he promised they would sign a striker.
"You can make promises, but you need to know the deal that makes them. Phone calls were made, the offers were made, it didn't get to them, whatever the reason," Dyche said.
"We can have debates on why (but) I'm not going to sign players for the sake of it.
"They've got to be good enough to affect what we do.
"There's good players here. They may not have shown, but we need to remind ourselves of the good players here. We've got to polish them up a bit."
Dyche also admits he is a "Marmite" choice who would probably not have got the job had the club not been facing a second successive relegation battle.
The former Burnley boss takes over with the club only staying off the bottom of the Premier League on goal difference after nine defeats in their last 12 matches.
He was not Moshiri's first choice - nor would he have been that of the majority of fans - as the billionaire owner wanted ex-Leeds manager Marcelo Bielsa, only for negotiations to break down over the Argentinian's terms.
Dyche, sacked by the Clarets last April after nearly 10 years at Turf Moor as the club headed towards relegation, joins with Everton engulfed in a civil war with supporters planning more protests against their perceived failure of the board to run the club correctly.
They are not the ideal ingredients with which to plot a path away from the bottom three, but Dyche, who accepts he may have to win over fans, is ready for the challenge.
"I'm a Marmite manager anyway - not everyone wants you," he said at his first press conference.
"Possibly if it (the club) wasn't in the shape it's in I wouldn't get the chance. I don't mind that. I'm a custodian. I won't be here forever but I'll look after it.
"I've got to earn my spurs and I'm willing to put the hard yards in to earn their respect.
"I'm aware of the recent noise around the club but I'm learning about the Evertonians and the reasons why.
"One thing I know is they stand by their club, protect it and support it - my staff and players need that."
Dyche will demand hard work as a minimum from a squad which has just one victory in the last 14 matches in all competitions.
But it will be changing the mindset which could be key, with Dyche famously claiming last April when his Burnley side were 2-1 down to Everton at half-time that the Toffees "didn't know how to win". The Clarets eventually won 3-2.
The new Everton manager insists his comments were misinterpreted but will work on improving their chances of victory.
"I've been through those stages. You get those feelings, those nerves, the feeling of a win coming gets the better of you - that's what I was referencing," said Dyche, who faces a baptism of fire at home to league leaders Arsenal on Saturday.
"Absolutely zero disrespect for Frank and his team. We've got to teach them how to win.
"There's a reasonably mature group here, they know the feeling of how to win, there's feelings of how we can help them with that.
"I've been in spells where you smell it on your team, they're desperate for the final whistle almost. I know why it comes around.
"You need to correct it, it's not easy, sometimes it's a twist of fate. You want it by design and we have to design a way and create that winning atmosphere and knowledge how to win."