ashed home a brace.Everton, however, will regain the advantage should they produce a positive result at home to Crystal Palace on Wednesday evening.
The race for the final Champions League place is set to go to the wire and Szczesny insists it does not matter how the FA Cup finalists secure it, so long as they do.
"The energy level was not great after playing 120 minutes (against Wigan at Wembley) on Saturday, but it was important to get three points," said Szczesny, who was back in the side having been on the bench for the semi-final, where Lukasz Fabianski saved two penalties in the shoot-out.
"In the Premier League we had not won in four games, so it was important to get back to winning ways - three points is all that matters at the moment.
"I will take four or five more games like that until the end of the season
As long as we get three points, it does not have to be beautiful.
"Every game is like a cup final for us now and we know we have to get the result every time and wait for Everton to drop points."
Szczesny is confident Arsenal can secure a positive end to a campaign which had promised so much.
"Before the four disappointing results we had recently we were still in the title race, so it has slipped away from us," the Poland international said.
"But it is important for us to fight for the new challenge, which is the top four now
We are confident we are going to do the job."
Giroud went some way to answering his critics - who had plenty of ammunition following a fluffed first-half chance when clean through on goal - with a strike of the highest quality.
Having held off both Andy Carroll and Winston Reid, the Arsenal striker expertly collected a looping ball into the penalty box from Thomas Vermaelen on his left before slotting it through Adrian's legs with his right boot.
Giroud paid his own respects to the Hillsborough victims, kissing the black armband and then looking to the heavens.
"I heard everybody talking about it before and I didn't exactly know the story until a few days ago, but I just wanted to pay homage to them," the France international said.
"It is something which made me feel consoling and I wanted to dedicate my goal to the families involved."
West Ham, meanwhile, must now regroup for Saturday's visit of Crystal Palace, when they will be out to avoid a third successive defeat and make their Premier League status completely secure.
Midfielder Mark Noble said: "We cant keep putting on good performances against the top teams but then not getting anything
I would rather play bad and get some points.
"Now we have a big match at the weekend against Palace, so we will have to rest and recover for that and go out to put another performance in.
"Tony Pulis has changed things around there but we have been in good form at home and did well here at Arsenal, so we need to take that into the Palace match."
Source : PA
Source: PA