Allardyce, who spent much of the match giving the fourth official a difficult time, took enough time out to see enough of the game to say: "I'm absolutely totally and utterly flabbergasted that we didn't leave Burnley with a victory under our belts. From the very start, we had chance after chance after chance and then incredibly went 2-0 down. Even then, we had a couple of chances before half-time that we couldn't put in the back of the net.
"We slipped up defensively on a couple of occasions and they've scored two goals completely against the run of play after playing so well.
"We changed the system a bit and went for it a little bit more. The comeback was fantastic but it wasn't really a comeback because we were already there. We increased the amount of opportunities we could score from, but unfortunately we fell foul of not converting our opportunities into goals.
"We must have had four or five one-on-ones, we've hit the post and had a goal disallowed. We had 20 attempts and eleven shots on target and Burnley's total was five shots on target in the entire 90 minutes and they've scored two goals.
"Our first goal was a brilliant goal from Kevin Nolan from the hardest chance we created - it wasn't even a chance - and James Tomkins converted from a great free-kick.
"It's just incredible that we dominated possession for the whole 90 minutes and created chance after chance and still ended up drawing 2-2. We're all distraught after such a performance with such great quality, but unfortunately even when did find the net, the referee decided we couldn't have it and when we didn't the post decided to stop it!
"It continues to go on and on and we just cannot find that final way through to the valuable three points we're after. With such a top, top performance, the disappointing thing is the top line 'Burnley 2 West Ham 2'."
He continued: "Anybody who watched the game will see what we've done and what Burnley have done. I've never dominated a game like that away from home. We beat Watford 4-0 and dominated the game but we dominated this game a lot more than that.
"Ask any question about what we're not doing and it's converting our chances into goals. It's going to cost us very dearly if we don't sort it out as quickly as we can.
"We can take a lot of heart out of the quality in this performance, but the bottom line is that we're down to single figures in games remaining and there is no making-up time now. Whether we play better than the opposition or it's an even game we've still got to win.
"When you dominate a game like we dominated this one, you've got to bury the opposition - 5-2, 6-3 or 6-2 would not have been a flattering scoreline for us.
"We're very disappointed and I'm sure Burnley were very grateful to hear the final whistle.
"The players have got to find the courage to take their chances. They have got to have the nerve, composure and professionalism to convert them into goals. We cannot wait any longer. We've got to put the ball in the net when we get the chances. Our conversion rate has to be a lot better.
"To be honest, I'm only saying what I've been saying all season, but it's a lot bigger now. We've had more chances than we've had all season, but our goal tally is getting less and less instead of more and more and that is the concern at the moment.
"We should have got a victory on Saturday, but we didn't get it so we know only two wins in the next two games will be enough to get us above Reading.
"When you entertain the fans, they are going to sing, and we entertained them apart from conceding two very sloppy goals which is not like us normally.
"The performance for 90 minutes, people might try and say it was a second-half comeback, but we completely dominated Burnley. It's just unbelievable that we haven't won."
Eddie Howe didn't quite see things the same way as Fat Sam, and I'm not sure anyone else did either.
Howe said after the game: "For the neutral it was probably a great game, but for me it was tough to watch, especially as the second half wore on. For 60 minutes I thought we were really, really good against a top side who I think will be a Premier League team next year.
"I felt we ran them all the way, but once they got the goal the game changed and we were on the back foot, struggling to contain them. It all stemmed from conceding that goal because I felt we were going to see the game out quite comfortable in the end, but that lost us the game really.
"In the end Lee Grant had to make some great saves, but we are disappointed because I feel that in a few months, that team would see that game out winning comfortably."
Howe included Steven Hewitt on the bench today with numbers down and he also explained the absence again of Jay Rodriguez.
"Jay wasn't anywhere near," he admitted. "He felt his groin again at Ipswich and he hasn't trained since, so we had to leave him out. It's nothing serious, but his enthusiasm to play against Ipswich, when he probably shouldn't, has cost him.
"I was also delighted to give Stevie (Hewitt) his first game on the bench. It was a difficult one to throw him into, even though I was tempted.
"It would have been a real physical challenge and I want to make sure we blood him at the right time in the right game, but there's plenty more to come behind Stevie and they might get a chance.
"We only have a small squad, with two injured players out of the squad today, so hopefully they can get more involved between now and the end of the season.
"Today though was all about getting a performance and I think we got that. Hopefully the supporters can see how hard the lads worked and that the group mentality is very good. They would have seen that we are trying to play the right way. It's the hardest way, but ultimately the right way.
"For us, it's about trying to find that consistency. We've had a very bad run at a terrible stage of the season that has cost us, so we need to learn from that for next season."