First-half strikes from Callum Glen - his first of the season since moving to the club from US Portsmouth in the summer - and defender Tom Cain were followed by teenage substitute Evan Harris' clincher after the restart as the Moneys ran out 3-1 winners at Blackfield last night.
The victory was a welcome one, with Moneyfields winless in their previous three league outings - all of which were against sides in the division's bottom eight positions.
But Quirke - taking charge alongside fellow assistant Paul Barton with manager Glenn Turnbull away on holiday - insisted Moneys cannot afford to stand and admire a 'much, much improved' performance.
Instead, he is demanding the squad show exactly what they are capable of with a trip to table-toppers Hamworthy on Saturday in the league followed by a tricky Russell Cotes Cup semi-final at Brockenhurst next Tuesday - themselves currently sitting third in the Wessex Premier standings.
‘It’s all well and good being on the wrong end of three or four results and saying, ‘lets put it right lads, lets get ourselves together and lets deliver something that’s quality,’ the next challenge is stringing that form together - hopefully they can do that,’ said Quirke.
‘Nobody wants to be involved in a group who lets the season fizzle out. The reality for us is we’ve got a great challenge on Saturday to play a team top of the league and in the last-eight of the FA Vase and go there and put a marker down.
‘It comes thick and fast because on Tuesday we head down to Brockenhurst who unluckily, I think, got knocked out of the FA Vase in the last-16, who are still a decent, well organised, good outfit in the semi-final of a cup.
‘It’s not like there isn’t anything to play for, certainly in the next couple of games, it doesn’t need any external motivation from us - these aren’t middle of the table dead-rubbers. These are games which will affect our thinking for the future, affect where we finish in the league and may well get us to a final.’
Moneys appeared on course to record a comfortable win at Blackfield when Glen's first of the season and Cain's 24th-minute header - both arriving in the space of five first-half minutes - had put the visitors two goals to the good at the break.
Yet there was slight cause for concern after Owen Fee reduced the deficit on 57 minutes before Harris' left-foot volley ensured victory for Moneyfields 15 minutes from the end of normal time.
Quirke added: ‘It was a much, much improved performance on the past four, really, where we’ve not done ourselves any justice. It was really pleasing to see that level of performance we did last night.’