He stresses that there is no lack of motivation, even if getting another 15 points, tall order that it is, would hardly be likely enough to qualify.
With Newcastle, in fifth, and Leeds, in sixth, just two and four points respectively from the Hammers' absolute maximum of 61 points there is an almost unsurmountable number of points to be made up.
This can largely be put down to the away results, of course, which have dented the goal difference as well as the points tally.
As reported here last week, seventh place can be no guarantee of a UEFA Cup place even if England is assigned one of the 'fair play' places, and Arsenal and Chelsea, both likely to finish in the top five, contest the FA Cup final, thus sending a UEFA Cup place to sixth.
Nonetheless, there has been much discussion about the matter, so, to clarify, here is an official statement from UEFA on the subject:
'In its efforts to promote fair play, UEFA establishes fair play rankings for each season based on all matches played in all UEFA competitions (national, representative, and club teams) between 1 June and 31 May.
In establishing these rankings, only those associations whose teams have played at least the required number of matches (total number of matches assessed divided by the number of associations) are taken into account.
For this purpose, fair play conduct is assessed by the appointed UEFA match delegate. In reward for the fair play example they set, a maximum of three associations which attain a previously defined standard (average of 8.0 points or more in the rankings) each receive one additional place in the UEFA Cup of the next season.
These additional places are reserved for the winners of the respective domestic top-division fair play competition. If the winners of the domestic top-division fair play competition have already qualified for a UEFA club competition, the UEFA fair play place goes to the highest team in the domestic fair play rankings which has not already qualified for a UEFA competition.'
As West Ham are not in the upper echelons of the UEFA fair play league - as distinct from the simpler fair play league which appears in some newspapers but is only based on fouls, yellow, and red cards - the chances of qualifying for the UEFA Cup in this way are between slim and none.
As finishing sixth in the league is also all but impossible because of the 11 point gap between the Hammers and the current incumbents of that position, Leeds, European competition is something of a dream, but David insists: "It is tremendous to be seventh with a game in hand. Everyone keeps saying it is against Arsenal but ultimately it is a game in hand.
"We are clear of the other sides and if we continue the form I see no reason why we can't finish in seventh. I'm confident, that's what I'm looking for, and the rest of ths side are equally as confident - and equally as focused.
"We are looking to win five games and what happens, happens - as long as we do what we can do then we give ourselves a chance.
"If other things materialise we want to be in that position to reap the benefits, but as a team we have got to keep performing.
"It is has got to be on our minds otherwise we could retire and leave the season alone now if we are not looking to get something out of it.
"We are not going down so there is an excuse if they want to take that road but I'm not looking that way and the buzz in the changing room after they realised Tottenham had lost was fantastic."
UEFA's criteria for fair play points, as marked by an assessor at each game, are fascinating.
The deduction of one point for a yellow card and three for a red is straightforward enough - a player would lose his club four points if he was booked then given a 'straight' red card later, but other criteria are much more open to interpretation.
'Positive play' points, from a minimum of one to a maximum of 10, include 'positive aspects' such as 'bringing the ball quickly back into play even when in a winning position' and 'negative aspects', such as what UEFA call 'play-acting'.
'Respect of the opponent' brings a maximum of five points though 'blameless behaviour but without any particularly positive attitude or gestures towards opponents should be assessed with a mark of four rather than five', they say.
'Respect of the referee' is indicated as concerning them 'as people as well as for the decisions they take' and includes 'the acceptance of doubtful decisions without protest.'
'Behaviour of team officials' [who are expected to 'make every effort to develop the sporting, technical, tactical, and moral level of their team through all permitted means') is another criterion.
'Behaviour of the crowd' is another factor; 'the crowd is considered to be a natural component of a football game', say UEFA, who also state 'the crowd is not expected to watch the game in silence' and that 'they should appreciate the performance of the opposing team, even if they emerge as winners'.
However, the behaviour of the crowd is 'applicable only if a substantial number of fans of the team are present' - and if they are not, that item is disregarded, bringing the maximum score of 40 down to 35.
When the assessor has given his marks, the points given for the individual components are added up, divided by the maximum number of points, and multiplied by 10.
You might want to try it yourself some time!