Sturridge, 25, is not in Hodgson's latest squad after suffering a thigh strain on England duty last month.
Reds boss Brendan Rodgers criticised England's handling of the player, and did not want him to be called up for games against San Marino and Estonia.
"It's simply a fact, an unfortunate fact, that he's not recovered," Hodgson said of Sturridge's absence.
"There's no problems or conflict there at all."
Sturridge has missed Liverpool's last six games but there is a chance he could return on Saturday, against West Brom in the Premier League.
But Rodgers said he would not be able to play in the Euro 2016 qualifiers with San Marino on Thursday, 9 October and three days later against Estonia.
"I've had good communication with Roy and we spoke at length on the situation," said Rodgers, whose side were beaten 1-0 by Basel in the Champions League on Wednesday. "It was amicable. There is no issue.
"We had agreed it was probably too soon for Daniel to meet up with England irrespective of whether he was involved this weekend or not.
"Every individual player is different. I respect he (Hodgson) had work to do internationally but my thoughts are with Liverpool players and what their needs are.
"Daniel hasn't trained with the team at all since the injury with them and it was probably not the right time to go with them.
"I've not spoken to Daniel. My focus is on Liverpool, it is not on England. I spoke to him about being available for Liverpool but I can't think about England when he is not ready to play for Liverpool."
Hodgson said there had been "no question" of selecting Sturridge for the double-header.
"He's not played for Liverpool at all since picking up the injury with us. As I understand it he's still got some work to do before he's fully fit," Hodgson said.
"It's a great blow to us, Liverpool and the player, because he was anxious to be a part of these two games."
Sturridge has made 16 appearances for England since making his debut almost three years ago, scoring five goals - his most recent coming in the 2-1 defeat by Italy at the World Cup in June.
England won their opening Euro 2016 qualifier 2-0 against Switzerland last month.

The Sun reported that it was offered the images, which it said included shots of the duchess's children, Prince George and Princess Charlotte.
The paper said someone had contacted it asking for Â£50,000 within 48 hours.
The Met Police said inquiries were ongoing and no arrests had been made.
The haul from the hack is believed to include 3,000 pictures, and an anonymous person has reportedly tried to sell them via encrypted messaging service WhatsApp.
The Sun quoted a spokesman for Miss Middleton, who was maid of honour at her sister Catherine's 2011 wedding, as saying: "Thank you very much for drawing this to the family's attention.
"I can confirm that not only have the lawyers been informed but the police are about to be involved as well."
A Met Police spokesman said: "Police have received a report concerning the alleged hacking of a personal iCloud account. Specialist officers are now investigating."
In the summer, Miss Middleton and hedge fund manager James Matthews confirmed their engagement, with a wedding planned for next year.
Several high-profile figures have had images stolen from their iCloud accounts, including actress Jennifer Lawrence and singer Rihanna.
In July, US man Edward Majerczyk pleaded guilty to running a phishing campaign to steal private pictures and videos from film and TV stars, in what was known as the "celebgate" affair.
In 2014, Apple said it had expanded its use of "two-step verification" checks to protect data stored on its iCloud servers.
The process works by introducing an extra step after an account holder has typed their username and password into a device they have not used before.
They are also required to enter a four-digit code that is either texted to a trusted mobile phone number or sent via Apple's Find My iPhone app.
If the person does not enter the code, they are refused access to iCloud and are blocked from making an iTunes, iBooks, or App Store purchase.
England manager Roy Hodgson has rejected talk of a rift with Liverpool over injured striker Daniel Sturridge.
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Police are investigating claims an iCloud account reportedly belonging to the Duchess of Cambridge's sister Pippa Middleton has been hacked and private photographs stolen.