They accounted for 8% of the entries answering the question posed by host Vernon Kay, who asked: in which gameshow would you hear the phrase "Our survey says ...". The answer was 'Family Fortunes'.
They received a text back, asking them to text ITV with their contact details; however, the glitch was that they did not get this text until after the deadline to respond.
ITV has now decided to enter the 10,000 viewers who lost out into a second prize draw, which will have the same prizes, worth £25,000, as the original draw.
An ITV spokesman said: "This was an isolated ITV problem and one that was picked up by our mobile phone service provider as part of the normal monitoring process. We apologise to viewers affected by this problem."
Public confidence in broadcasters' phone-in quizzes and polls has been knocked after several such incidents were reported in the wider media.
Last month, the BBC had to apologise after it emerged that a 'Blue Peter' phone-in had been won by a studio audience member who had been told to ring in by producers after other entrants had been hit by technical problems.
The premium-rate telecoms regulator Icstis is currently investigating four shows: BBC One's 'Saturday Kitchen', Channel 4's 'Richard and Judy', and ITV's 'The X-Factor' and 'I'm a Celebrity ... Get Me Out Of Here'.
Ofcom is also conducting an investigation.