Hodgson and Liverpool boss Brendan Rodgers have entered a war of words, with Sturridge having been unavailable for the Premier League side since suffering a thigh injury.
Rodgers was unhappy with England's treatment of Sturridge, who he wanted following the recovery programme the club put in place.
Speaking on Thursday, Hodgson said Sturridge was eager to train during the session in which he got injured.
"The interesting thing for the session where Daniel got injured is that he was quite keen to take part because he was such an important part of it, and we were trying to develop a new system of play," Hodgson said.
"He was the forward who understood it best. He was more than happy to come in and help us to get our points over.
"I understand Brendan being unhappy. We are never happy when we send a player back injured, but we do our best."
Hodgson denied his relationship with Rodgers had suffered, but is unhappy with suggestions Sturridge asked not to train and needed 48 hours of recovery.
If Sturridge plays for Liverpool against West Brom on Saturday, Hodgson said the player's fitness would "be a matter for some discussion".
Rodgers had also expressed concerns over the fitness of Raheem Sterling, but the Liverpool attacker was selected in Hodgson's squad.
Hodgson said he needed to select the best available players, as his side prepare to face San Marino and Estonia in Euro 2016 qualifiers.
"I need to win games, just as he does. I need my best players," he said.
"He [Sterling] has played quite a lot but there must be six or seven who have played as many minutes.
"I do not expect managers to tell me whether players should be selected, no more than I would dream of telling them who to pick."
Thank you for reading 5 articles this month* Join now for unlimited access
Enjoy your first month for just £1 / $1 / €1
*Read 5 free articles per month without a subscription
Join now for unlimited access
Try first month for just £1 / $1 / €1