Regular skipper Wayne Rooney was not named in Gareth Southgate's squad due to a lack of recent match action, while Liverpool captain Jordan Henderson was ruled out through injury.
Chelsea centre-back Gary Cahill took the armband during England's 1-0 friendly loss in Germany on Wednesday but was suspended as recalled striker Jermain Defoe and substitute Jamie Vardy got the goals to strengthen the Three Lions' position at the top of Group F on Sunday.
Manager Southgate has floated the idea of appointing his captain on a game-by-game basis and praised Hart's leadership qualities in the build-up to his 70th cap, but the 29-year-old would be happy enough for it to be a one-off.
"Wayne Rooney's our captain, I know that. And then I'd imagine Hendo and Gaz… I was just last-man standing," Hart told ITV.
"It's obviously a proud moment to captain your country but I know my place in this team.
"I just want to keep trying to perform to the best level."
Aside from Defoe notching a first international goal for four years, the Wembley crowd witnessed some forgettable fayre, with Lithuania's lack of ambition and England's sluggish early tempo contributing to a paucity of goalmouth action.
"It wasn't pretty, was it? But we got the goals we wanted," Hart said.
"I think they are a better team than maybe they gave themselves credit for.
"They were quite happy not conceding many and then seeing what happens. They are frustrating afternoons for everyone.
"We'd like to have scored five or six but we didn't. We're top of the group and our goal is Russia."
Lithuania's defensive ranks were well stocked from kick-off and Hart was grateful to have Sunderland striker Defoe on hand with his killer instinct to chalk up a 20th England goal after 21 minutes.
"It's what he does, I don't think anyone would ever question that about Jermain," he added. "Vards was brilliant on Wednesday night, he worked so selflessly for the team.
"Jermain got the nod today because we knew we were going to need a killer in those situations with all their defenders in the box.
"Vards came on and just settled the game for us. It's a really nice combination to have.
"From looking at the start of the week, we've had a lot of strikers injured but to have that quality and those goals are nice."