Swansea’s Lita was a success on loan at Hillsborough last season, and had been tipped to return.
But Jones instead brought in Hull’s Fryatt on loan and revealed the striker’s match fitness was the decisive factor.
“Leroy was on the radar,” admitted Jones. “It was going to be Leroy or Matty, and we felt Matty had played games and was at a better level of fitness to suit us in the short term.
“We had to wheel and deal and that’s what we’ll continue to do.”
Fryatt, 27, netted on his full debut in the 1-1 draw at Brighton and was unlucky not to score in the draw with Ipswich Town.
“He looks as if he’s coming back to his best,” said Jones. “He looks sharp in training. It’s a gamble you take when you bring in loan players.
“I haven’t spoken to Stevie (Bruce) yet about what happens when Fryatt’s month is up. When the time is closer, we’ll do it.
“In his two games, he scored against Brighton and was unlucky against Ipswich. Strikers need games and goals. His ratio at the moment is one in two so I think he’ll be happy with that.”
Lita – yet to play this season after six goals in 13 starts for the Owls last term – this week joined Brighton on loan, with Jones deciding to bring in reserve goalkeeper Damien Martinez from Arsenal to provide competition for No 1 Chris Kirkland.
With back-to-back games at Bolton and Barnsley in the next week, Jones feels his players can escape the pressure to perform that Hillsborough can bring.
“For whatever reason, I think we’ve had better performances away than at home,” he said.
“Players should want to play at home. It’s not a case of them not wanting to do it, but maybe one or two are feeling a bit more relaxed away from home.
“The pressure sometimes grows and grows because you haven’t got the result. In the end you’re more worried about not giving the ball away – a natural footballer would just play and pass and not worry about whether the pass is going to get there.
“More importantly, we just have to keep working at what we feel will benefit us as a team.”