Jones, whose readiness to call up overseas-born players has attracted criticism, said his options were limited by the departure of players for the British and Irish Lions tour to New Zealand and that his focus was on the 2019 World Cup in Japan.
"It's not my job to worry about how they qualify, it's my job to pick players that qualify," he was quoted as saying by the Times. "I don't care how they qualify, I'll pick them.
"That's the rules we play under. I obey them like a good schoolteacher does. I don't control who qualifies and who doesn't. It's not my job."
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Heinz, Woodward and Schonert all qualify to play for England via a grandparent, while Solomona is eligible on residency grounds.
"My job is to pick players who qualify to play for England. We're missing 15 Lions, we're missing Saracens, Exeter, Wasps, (Leicester) Tigers, Northampton... who do you expect me to pick?" Jones added.
"Tell me. Who is there? I look at everything... You're suggesting I haven't done my homework. You are.
"I'm picking the best players available to play for England. In some positions we are down to eighth or ninth choice. We never know when we might need these players.
"We might get to the World Cup in 2019, have a final and need to find a fifth-choice number nine (scrumhalf). Now I know."
(Reporting by Simon Jennings in Bengaluru)
