The 19-year-old's knock was a record-high for a number 11 batsman and his final-wicket stand of 163 with Phil Hughes also broke a world record.
He admitted that he was delighted with his performance despite being caught by Graeme Swann just two runs shy of his century.
"It's been a great day," Agar told Sky Sports News. "It's probably the best day so far in my life. I'm rapt.
"I hit [the final ball] a bit better than I thought I was going to actually. Look, I was really happy. In all honesty I didn't really think I'd come out and make 98, so to have that happen on my first day is fantastic.
"It was good to get the team out of a bit of a sticky situation and get a bit of a lead."