Jermaine Easter scored his first goal for the Dons but Billy Paynter's brace, Jon-Paul McGovern's audacious lob and David McCracken's own goal gave Swindon a 4-1 win.
Robinson said: "We're obviously disappointed. It's a shame we went out because we were looking forward to progressing and possibly playing against some higher-league opposition.
"But we have faith in the players, we know it was just a one-off. It won't happen again. With the quality of players who made the mistakes, they won't make those mistakes again.
"Our performance was better in the second half and we can't wait for Saturday now - the players want to turn the tables."