Aston Villa boss Martin O'Neill and Everton counterpart David Moyes both admitted Arsenal are now red-hot favourites to claim the fourth Champions League spot after seeing their sides share a thrilling 3-3 draw at Villa Park.
O'Neill watched Villa recover from 3-1 down to salvage a point but it was the result neither side wanted in their uphill battle to overtake the Gunners.
Gareth Barry's penalty ensured Villa remain a point ahead of the Toffees but they are now eight adrift of Arsenal, who also have a superior goal difference, with just six games remaining.
O'Neill said: "I thought we should have won. Even at 2-0 and 3-1 down, we fought back. We showed great character and determination.
"But will obtaining fourth place now be hard? I wouldn't disagree with that. One of the two of us had to win. It is a result that definitely suits Arsenal.
"From that viewpoint, it is disappointing but we shouldn't just give up the fight.
"Arsenal still have some very tough games, so have we. We just have to win them. If we win every game, it will give us quite a few points and Arsenal still have the top three to play.
"This is where the excitement comes from. It is trying to compete and wanting to compete. In the last two years, we are averaging 40,000 gates. Villa are resurgent.
"This season we got ourselves into fourth position for a number of weeks and it was exciting and Arsenal were definitely in a fight. We now have to keep going."
Moyes was similarly dubious about his side's chances of joining the top four.
He said: "Arsenal's result at Wigan yesterday (a 4-1 win) made it very difficult for any of us to get up there.
"If Villa had beaten us, they would have still been in with a shout and if we had won, we wouldn't have given up the chase.
"I don't think you give up the chase until it is mathematically impossible but I think, if we are being realistic, it will now be very hard.
"Everton and Villa have tried hard to push the top boys but maybe have come up just a little bit short.
"We have got to keep trying to do the job and finish fifth and, if you had given me that at the start of the season, I would have said 'yes', especially with what we have been missing player-wise - and missing today as well."
Meanwhile, Villa are sweating on the fitness of joint top scorer Gabriel Agbonlahor after he suffered a hamstring injury during Sunday's draw.
Agbonlahor, who has netted 13 times this season, limped out of the action during the second half and will undergo a scan in the next 24 hours to determine the extent of the problem.
Villa manager Martin O'Neill will be keeping his fingers crossed Agbonlahor's spell out of action is minimal as he is already without the injured Emile Heskey.
Agbonlahor confirmed: "There is something wrong with my hamstring. I don't know what it is. We'll have to wait and see the results of a scan.
"I got the ball and pulled up and came off as a precaution. I don't know how long I'll be out for.
"It felt pretty sore during the game but I came off when I did because I didn't want to make it worse."
O'Neill revealed Agbonlahor had defied a virus to play before his hamstring blow.
He said: "Gabby played against Everton after not training for the two days before the game. He had not been feeling great.
"But we always knew he wanted to come out and play and this is one of the big things about him and Ashley Young and a number of the other lads - they want to play.
"When Gabby came off, his hamstring was sore. Everything was wrong with him in terms of not being physically fit for the game but he still did great. That is the kind of character he is."