Oxtoby’s side twice fought back to equalise against their Nations League Group B1 rivals in Gyor before Hungary snatched a winner deep in stoppage-time.
Simone Magill’s late penalty appeared to have rescued Northern Ireland a point, but Hungary defender Hannah Nemeth struck in the fourth minute of added time.
Caragh Hamilton’s late header cancelled out Viktoria Szabo’s first-half opener for Hungary, who had regained the lead through Dora Sule’s stunning long-range effort.
Oxtoby, whose side play Hungary again on Tuesday in Belfast, said: “I’m really proud of the players in terms of the determination they showed and the flexibility with some of the tweaks and changes we made in the game.
“We showed great resilience to come back a couple of times there, but we’ve got to see the game out.
“You can tell by both teams’ reaction, our disappointment and their jubilation at the end, how tight the game was and we’re really disappointed we let it slip.
“But we get an opportunity to play them at home now and we’ve got to look forward and focus on that.”
Hamilton headed Northern Ireland level with her first touch after stepping off the bench, while Magill was also a second-half substitute.
Oxtoby added: “We talk a lot about it taking an entire squad. We don’t just talk about it, we act on it.
“We spoke before the game, you look at the state of the pitch and the conditions and it was going to take a squad effort.
“The starters put in a great shift, but we felt we did need a little bit more off the bench and Caragh and Simone injected that and I thought they were fantastic.”