Robinson was denied a famous cup triumph by an 89th-minute equaliser from QPR substitute Heidar Helguson.
While Robinson will get another crack at QPR in the replay a week on Tuesday, he was anxious to put the enterprising 1-1 performance of his side, who are well placed for promotion to the Championship this season, into sharp perspective.
And he chose to highlight Mancini's moan earlier in the week that he was concerned his Premier League title plans could be hampered by a shortage of players.
Robinson said: "I thought Mancini's comments about not being able to field a team with £350million (of talent) was embarrassing.
"I spent £35,000 on (striker) Charlie MacDonald and have got two 16-year-olds on the bench. Come and have a go at this, see how you feel.
"I can't spend £100million on players in the transfer window. I might go and get one or two cheeky loans. I believe those players deserve a shot at this league. I'm proud of them but gutted about the result."
Dean Bowditch gave MK Dons the lead after Iceland striker Helguson, who had come off the bench to replace DJ Campbell on the hour mark, was dispossessed in his own penalty area.
However, Helguson made up for his error by firing the equaliser in the closing seconds while QPR were down to 10 men, with Alejandro Faurlin having sustained a knee injury after manager Neil Warnock had used his three substitutes.
Warnock is convinced QPR's combination of fortune and character could be the turning point in what has been a tough first half of the season.
He said: "Heidar's just had a blemish, but he made up for it and you could see what it meant to the lads. Things like that change seasons.
"All credit to the boys, they kept going and I am delighted. People talk about did we want a replay, well yeah we did.
"At 1-0 down with 10 men and going into the last few minutes it's a great result for us. You need a bit of luck in the FA Cup, all the big teams do."
Warnock revealed another benefit of the replay at Loftus Road a week on Tuesday.
It means captain Joey Barton, suspended on Saturday after starting his three-match ban for his dismissal against Norwich, misses just one more Premier League match against Newcastle next Sunday before missing the replay but being eligible for the crucial relegation clash with Wigan on January 21.