The Irish, who were 34-6 winners over Wales in Perth, have been one of the successes of the tournament but lost out on qualification for the knockout stages to Papua New Guinea.
Aston pointed to the contrast provided by Samoa, who are in the quarter-finals despite gaining only a draw from their three games because three teams go through from their group.
“It’s disappointing and something that probably needs looking at,” Aston said. “We deserve to go through, I would suggest.”
Ireland captain Liam Finn was even more critical, claiming the format lacks logic and could hamper the drive to attract new supporters to the game.
“It doesn’t make sense,” Finn said. “Try and explain that to someone who’s not in rugby league — that’s how you judge it. I’ll go home and tell someone we won two games and didn’t get through and another team got through from drawing one.
“How do you attract new fans when that’s how you explain the game to them?”
Second-row forward Oliver Roberts scored two of Ireland’s six tries and Finn contributed 14 points as they overcame sweltering heat to condemn Wales to a third straight defeat.
Aston revealed afterwards that the game brought the career of former St Helens, Hull and Hull KR full-back or winger Shannon McDonnell to an end.
“We wanted to win for him,” Aston said. “He’s been very good for us.”
Wales were left still looking for a first World Cup win since 2000 but their performances have come as little surprise after a spate of withdrawals left them with just three Super League players.
Finn said: “We don’t take any satisfaction from beating Wales by a decent score.
“They’ve been let down by a number of players who pulled out late and I really feel for John Kear and all the staff.
“There is a gulf because certain clubs don’t release their players from Super League. I don’t think it’s good enough, especially by the players who have got a leg up from the Welsh game.”