Sam Allardyce believes Saturday's match with Arsenal has shown that his new-look West Ham United side need to hold no fear when mixing it with the Barclays Premier League big boys.

The Hammers matched the Gunners for much of Saturday's sell-out encounter, but after Mohamed Diame had opened the scoring in the 21st minute, two fine second-half strikes from the visitors were decisive as they ran out 3-1 winners. Big Sam's side caused their north London neighbours a host of problems, however, and had they taken one of the number of good opportunities that had fallen their way, they could well have maintained their position above Arsenal in the table.

"We tried our best - that's all we can do," Big Sam said. "We weren't overran. We might have been a lot worse of in terms of possession - that's obvious - but in terms of chances created and shots on goal, it was very close indeed.

"Whenever my teams have won against top teams in the past we have always punished the opposition when we had the opportunity."

Diame's first goal in claret and blue is likely to be among the contenders for Goal of the Season at the 2013 Player Awards night, while Arsenal's third goal - a long-range effort from Santi Cazorla - was also worthy of praise, according to Allardyce.

"I'm not sure Cazorla's goal was better than Diame's. It was a great strike but Momo beat two players and then smashed it in the net. They were probably as good as each other.

"The quality of both goals was fantastic. It's a pity we couldn't show that quality with our chances in the second half.

In addition to testing the Arsenal backline, West Ham United once again defended their goal bravely and selflessly, with Jussi Jaaskelainen rarely troubled. Big Sam was pleased with what he saw and will be demanding the same level of performance when Southampton visit the Boleyn Ground on 20 October.

"For all of Arsenal's possession - which was fantastic considering the way they move the ball around - our defensive unit did a fantastic job and limited their chances.

"In the second half we wanted to do a little bit more in terms of testing their defenders. We did that but we didn't score and we paid a heavy price for that as they punished us at the end."

Andy Carroll's return to the starting XI was another positive from the afternoon and he carried on where he left off on his home debut against Fulham. After winning countless headers and working hard to not afford the Arsenal defenders any time on the ball, the West Ham No8 came close with two headers - one from a corner in the first half and another from a George McCartney cross in the second.

"That's why we've got him - he's an unbelievable player and he can only get better. For his second chance he outjumped the goalie. The goalie can use his hands to catch the ball but he goes and outjumps him.

"Anybody that doesn't fear Andy Carroll is foolish. As long as we can keep giving him the service I think he's going to be a tremendous asset."

Like a number of other first-team and Development Squad players, Carroll will be absent from Chadwell Heath this week as he reports for international duty with England. Despite him lasting a full 90 minutes on Saturday, Big Sam is hopeful he will return fully fit after the Three Lions' double header against San Marino and Poland.

"I'm not worried Andy could play for England as he is really lacking in match practise. What I will speak to Roy about is his fatigue level.

"Andy will be stiffer than everybody else after this because he hasn't played a full 90 minutes in recent weeks. So he will take a bit more time to recover.

"But he should be fine for Friday and hopefully he will get a game at some stage to improve his match fitness."

The international break will give Big Sam a chance to look back over an impressive start to lfe back in the top tier of English football, but also an opportunity to look ahead, with a tough run of fixtures on the horizon as the Hammers head into November.

"It's been a good start to the season and it's been exciting. We've gelled a bit quicker than I thought we would. We've got some real talent in the team with some good experience. Southampton is our next game and it will be a big test for us. We'll need to lift ourselves for that to try and get back on the winning trail again." 

Allardyce and his West Ham United medical staff are also likely to use the break to assess the extent of injuries picked up by Ricardo Vaz Te, Guy Demel and Winston Reid on Saturday. Vaz Te is looking like the most serious, with a dislocated shoulder set to keep him out for up to 12 weeks. Demel's thigh injury forced him off in the secon half, while Winston Reid suffered a back spasm that was still being looked at on Monday morning.

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