Doocy told "America Reports" on Thursday, shortly after leaving the White House, that he had a "binder-full" of questions for Biden.
"I mentioned last night on 'Special Report' I had a binder full of questions. I think some people thought I was kidding, I was not kidding," he said, holding up the binder.
"We had a lot, and most of the [subjects] he did not get to. For example, nobody asked him about this big plan that he's got ... to completely transform the economy to make it all green," Doocy said.
"That is something we were hoping to get on the board with and there were not a lot of questions about COVID, particularly the investigation into the origins of it," he added.
Doocy noted Biden has discussed at length his federal response to the pandemic but has not publicly considered investigating the origins of the virus, which first broke out in Wuhan, China.
While Biden was speaking, he noticed his top two press aides, Communications Director Kate Bedingfield and Press Secretary Jen Psaki, off to the side of the dais.
"They were monitoring what he was saying, it looked like they were checking their phones to get the instant reaction, but while he was up there he was pretty much on his own," Doocy said.
Doocy, who reported on Biden throughout his 2020 campaign, said the last time the president held an event like this was in Wilmington, Del., prior to being inaugurated.
Biden's first press conference falling on the 64th day of his term marks the latest date for such an event since President Calvin Coolidge in 1923.
Doocy said one of his takeaways from the presser was the president appeared to change his tone on the unity he promised in his inaugural address.
"It’s notable, though, for the entire length of the transition and the campaign before that, Biden was talking about how post-Trump, D.C. was going to be a less polarized place because he was a uniter. He thought a lot of Republicans were going to have an epiphany as soon as Trump was gone and want to reach across the aisle to work on progressive priorities," he said.
"Not only has that not happened, we know he has had very little if any outreach to Mitch McConnell and so it’s not clear where Biden thinks that is going to start: this convincing Republicans that they should be working with the other side."