FIFA's executive committee is due to decide later this week on the principle of moving the tournament, and is expected to agree that it should be moved from its usual time of June and July to earlier or later in the year due to the extreme heat during those months.
UEFA's 54 member nations have already backed a move.
Robertson, who was part of the delegation for England's failed bid for the 2018 World Cup in 2010 - at the same time that Qatar won the 2022 finals - also believes that those other countries who bid for 2022 should be compensated by FIFA.
He told Press Association Sport: "I don't think anybody in the world of football thinks a World Cup in Qatar in the summer is a sensible or deliverable option.
"To that extent, this is a mess of FIFA's own making.
"I don't blame the Qataris at all - they wanted the World Cup and every country is entitled to have that ambition and they entered the bidding competition in the way suggested by FIFA. I entirely blame FIFA."
The minister, who admitted that the Government's relations with the world governing body had deteriorated since 2010, also said there should be no disruption to the football seasons either side of 2022.
He added: "I don't have much of a relationship with FIFA. I have a good one with UEFA but we did say in 2010 after the 2018 World Cup bid that we didn't wish to deal with FIFA again until they have reformed their governance.
"I also don't see that moving this [moving to winter] should be allowed to disrupt the years either side of the event."
Robertson said there would have to be "compromise on all sides" to de-congest the football calendar, such as no FA Cup replays and a reduced number of friendly international fixtures.
Opponents of the move are calling for a decision to be postponed until a full consultation has taken place, while Australia Football Federation leader Frank Lowy has called for FIFA to pay back the £30million it spent on bidding for 2022 if the tournament is moved.
Robertson said he sympathised with calls for compensation but does not believe there should be a re-vote for 2022.
He said: "FIFA has to remember there are a series of other countries who bid for that 2022 World Cup in good faith and are now going to find the goal-posts have moved.
"If it's held in the winter that's absolutely sensible but to have a re-pitch would be quite unfair on the Qataris.
"I think a deal should be done where the fact the Qataris won it fair and square is acknowledged but other nations who bid for 2022 are compensated in some shape or form, either financially or by hosting other FIFA tournaments."
An investigation last week into the treatment of migrant workers in Qatar flagged up numerous abuses, and 2022 organisers said they were "appalled" at the findings.
Robertson said London's experiences in hosting the 2012 Olympics had shown it was possible to construct facilities for major sporting events and still maintain the highest standards of health and safety, and that it was up to the international sporting organisations to demand that is the case.
He said: "I think that it is important that major sports competitions are delivered to the strongest possible ethical guidelines and I would encourage world governing bodies to help deliver that."