The Finn said his own performance as coach has not been good enough as the Tannadice outfit slipped to a 3-1 home defeat to fellow relegation candidates Hamilton Accies.
"It's simply not good enough." Paatelainnan told BBC Scotland.
"I always question myself, my fellow coaches and what mistakes I have made."
Goals from Grant Gillespie and a double from Carlton Morris ensured an easy win for Hamilton, despite a late consolation from Simon Murray.
The defeat means United's drop to the Championship could be confirmed next week when they take on their city rivals Dundee at Dens Park.
"I have been here a long time and work my socks off with the players," explained Paatelainen.
"Of course I have made mistakes and look at myself very closely. But like I said, I am in the same boat as the players and it is simply not good enough."
Paatelainen said he could not understand why his team began so poorly after hearing they had the chance to reduce the gap on second bottom Kilmarnock to five points after the Rugby Park side lost to Inverness Caledonian Thistle.
The United boss questioned: "How can it mean more to Hamilton than our boys?
"We said this was our chance. This was a great opportunity to claw back the difference to a level we could really put pressure on Kilmarnock.
"And then we are nowhere near the intensity or the desire to be on the ball. We should be really disappointed with that."
A group of around 200 United fans demonstrated outside the ground at full time, and the United boss said he sympathised with the fans and their frustrations.
"We deserve exactly whatever is given to us," he said. "It's not good enough. It's poor, we take the second prize out there individually when we go into battles.
"It's very difficult to make a winning team consistently if you lose your individual battles and are too soft consistently."
Meanwhile Hamilton player-boss Martin Canning was full of praise for his team as they eased five points clear of second-bottom Kilmarnock in the race to avoid the play-off spot.
"That's almost back to near our best," he said.
"It was a big game, for what was at stake in the game and results are the most important thing at this stage of the season. "

John Baird's cool finish from a tight angle proved to be the difference.
That lead was nearly added to when Will Vaulks hit the crossbar from 20 yards, then Morton's Declan McManus did the same from 30 yards.
The game ended on a low note with Falkirk's on-loan Norwich midfielder Conor McGrandles suffering a serious leg injury.
Apart from Ton midfielder Joe McKee almost scoring directly from a corner and Vaulks' looping effort at the other end, the opening exchanges at Cappielow matched the dull weather.
But the uncovered, wet Bairns fans had something to cheer about when Baird used all his know-how to net his 17th goal of the season in front of the away end.
The ball had been booted high into the air in Morton's box and Baird outmuscled home defender Conor Pepper as it dropped, before staying calm to place it beyond goalkeeper Derek Gaston.
Vaulks' technique was ideal as he watched a side-footed curler kiss the the top of the woodwork soon after.
Morton's McKee directed a header wide when well placed and on-loan Fleetwood Town striker McManus - a revelation for Ton last season - went closer with a dipping free-kick just prior to half-time.
Bobby Barr rifled in a low left-footed shot just wide of the far post and McManus tested Danny Rogers again as Morton pushed for the equaliser.
But clear contender for man-of-the-match Baird came closest to hitting the back of the net in the second 45 minutes, forcing Gaston to make a brilliant clawed save from his half-volley.
McGrandles - in his second spell at Falkirk - came off the worst in a crunching tackle with McKee near the end, for which the Morton player was booked.
It meant eight minutes of added time but the visitors held on to secure their first victory since 2 January.
Dundee United manager Mixu Paatelainnan says he is in the same boat as the players when it comes to criticism of the team this season.
[NEXT_CONCEPT]
Falkirk beat Morton to land their first win in six games, moving two points behind Hibernian in the Championship.