Hearts boss Robbie Neilson apologised to fans after admitting that a "bad day" at Motherwell makes it "difficult" to catch Aberdeen in second place.
The Edinburgh side had a chance to close the eight-point gap after the Dons' 3-0 defeat at St Johnstone.
"It was a bad day for us, and we didn't deserve anything," Neilson told BBC Scotland after a lacklustre 1-0 defeat.
"I am disappointed for the fans who came. I have to apologise for the performance. It wasn't good enough."
Neilson accepted that finishing second is a long shot with only four games left. Hearts have Celtic, Ross County and St Johnstone at home, with a trip to Aberdeen their only remaining away game.
"It looks like it is going to be difficult now," added the head coach. "We have to keep striving and we have got Celtic next week, but today was a huge game and it just wasn't good enough.
"We gave away a a bad goal and found it hard to get back into the game.
"We didn't create enough chances when we had the opportunity to shoot, we didn't cross it when we had the opportunity."
'The boys believe in each other' - McGhee
Neilson's mood was in sharp contrast to Mark McGhee, the Motherwell manager able to celebrate a seventh win in nine games since mid-February.
"We feel there are still things to play for - people are still looking for contracts, our league position and pride," he noted.
"The training performances this week were top drawer and we hoped they would take that energy and determination into the game. It gave them the reward and it was a fully-deserved victory.
"The boys have applied themselves and even at this late stage of the season they are playing with energy and pace.
"We had a difficult January but we stuck together and kept doing the same things. The boys are a good tight group and we are seeing that now. They are working for each other, they believe in each other and care a lot about each other."