Boateng felt the Tigers crumbled under the intensity of the situation against Burnley last week, slumping to a 4-1 defeat at the KC Stadium having taken an early lead against a team that had not won away all season.
The defeat, coupled with West Ham's win over Sunderland, means Hull face Birmingham at St Andrew's tomorrow second from bottom of the table and four points from safety.
Boateng said: "It was a bad, bad result. We worked so hard in the whole week as a team because we realised nothing but a victory would be good enough.
"Once we conceded an equaliser, I think the pressure of facing relegation in the eye got to most of our players. Therefore we never recovered.
"Previous games in the season, even when we conceded goals, we also picked it up, but after the equaliser we never looked like we were going to score and that was so disappointing."
He continued: "We've had meetings, we've spoken about the importance of staying in the Premier League, what effect it would have on the area, on people working for the club.
"Every day we come into training and they do whatever we ask them, so it would not be fair on those people if we failed to do our job on the field.
"It was a good meeting and everyone, if they didn't already, realises now it's time for men to stand up and be counted. There's no time for flair, now is the time to come out and work as hard as you can."
Birmingham were tipped to struggle on their return to the top flight but they have far exceeded expectations and remain in the top 10 despite a run of six games with a win.
Boateng, though, is hopeful Hull can send a message to their fans by breaking their away duck.
He said: "They are beatable. They just lost 5-1 to Manchester City and we beat Manchester City at home and drew away. On the day, it's the team that wants it most.
"Against Burnley, we were not the team that wanted it the most and that cannot happen. The chance we had has gone so now we have to make our own chance.
"We let the fans down big time, but we cannot apologise to the fans for last week because the pain will still be there. And believe me, we have had pain this week.
"The only way we can apologise to the fans is by putting down a performance with a result. It's no good performing well at Birmingham and getting beat."
The Birmingham match is at the start of a week that will go a long way to deciding Hull's destiny, with Aston Villa and Sunderland visiting the KC Stadium over the next seven days.
And it is Wednesday's match, where Hull will play the game in hand they have on all their rivals, that Boateng believes will eventually prove crucial.
"We've got a game in hand and that game in hand will decide our future. We've got two games and, if we can somehow get four points between Birmingham and Aston Villa, that would give us not a little bit of a chance but a huge chance," he added.
Boateng is out of contract in the summer but he insists Hull's future is all he is thinking about.
He said: "I haven't thought about my own personal future. I like being here but the priority has always been to keep Hull in the Premier League.
"If Hull want to have me here after that, I would rather be playing in the Premier League than the Championship, so the motivation for me is there."
Boateng still has stitches in his mouth after being knocked out in the defeat by Stoke a couple of weeks ago but he is set to lead the team again while Andy Dawson should start despite bruising to his leg.
Richard Garcia had a knee arthroscopy yesterday and is out along with Stephen Hunt (foot), Anthony Gardner (ankle), Kamil Zayatte, Amr Zaki and club captain Ian Ashbee (all knee).
Boss Iain Dowie has already stated he will make changes to the team beaten by Burnley.