Semi Ajayi and debutant Nobel Mendy scored as Jakirović's newly promoted Tigers claimed a first Premier League win of the season and their first league victory over United since 1974, a result the Bosnian described as vindication for a plan built around structure rather than star power.
"It means a lot, we were organised and it was very good for us," Jakirović told BBC Match of the Day. "The players stick to a tactical plan, we suffer because we play against Manchester United but we punished the opponent.
"We are one year together, we had three new guys and all together they looked like a team there and in the end we succeeded."
The manager was open about the disruption his side had to overcome, with a reshuffled back line forced into action against vastly more expensively assembled opponents.
"We had a lot of problems because we made four substitutions in our defensive line which is unusual. You have to play, you have to fight and maybe now we need more players."
Hull City travel into the season widely tipped to be involved in a relegation fight, and Jakirović used the platform to address that scepticism directly.
"This is football. We are professionals. We are trying to prove people wrong. I know there are 37 games to go but this is a good base for the future."
Speaking separately to TNT Sports, Jakirović reflected on the physical demands of a game his side spent long periods without the ball.
"I'm very proud of course because we were good with intensity and strength in the challenge. It wasn't easy because we knew we'd be out of possession and we could punish them also. We practiced our set pieces."
Mendy's opener arrived from a well-worked delivery, and the manager pointed to hours of preparation behind the goal.
"Very valuable for us this season, we struggled last season with them. I like it when we try to prepare something during the week and then it shows on game day."
Told after the match that Hull had not beaten United in the league in 52 years, Jakirović admitted the scale of the achievement had caught him by surprise.
"I didn't know, it's good to break a record."
The Tigers fielded several summer arrivals, including Mendy, and their manager stressed the value of settling new faces in quickly.
"Good concentration on the pitch, I'm very pleased with them because we have to know each other better."
Looking ahead, Jakirović suggested the win could have a knock-on effect in the transfer market as Hull look to strengthen further before the window closes.
"Even now, players we wanted, it might make their decision easier. We have to continue like this."