The Australian was cheered by the home fans during and after the game, having been told earlier this month that his contract will not be renewed at the end of the current campaign.
Asked whether he expected to see out his stay, Cartwright, who said he felt "betrayed and disrespected" by the club's decision, revealed he is set to thrash out his future in meetings with the club's hierarchy next week.
"I don't know," said Cartwright. "I've got a couple of meetings early next week and it will be a little bit clearer where we go from there. It's a difficult one. I certainly don't want to let that playing group down, but sometimes these things are not in your hands."
Home fans made their feelings on the decision plain during the match, cheering when Cartwright's face appeared on the big screen at the MKM Stadium, and backing him during his post-match interview on Sky television.
Cartwright admitted: "You don't expect that, it's not why you do the job, but I think it says a lot about the people in the town.
"I was told before I got here that as long as the team goes out and has a crack the fans will get behind them, and they have. The results aren't showing it at the moment but they've got a team they can be proud of. I see enough good things ahead for this group.
"The most important thing now is the club. The club is made up of its fans, so the most important thing now is that we all put the club at the very head of the list – that's what matters."
Hull started superbly with Logan Moy's early try steering them to a 12-6 half-time lead, but Saints came on strong after the break and late tries from Kyle Feldt and Harry Robertson eased the visitors to an ultimately well-deserved victory.
Saints boss Paul Rowley admitted his team struggled to cope with the hosts' early intensity and paid tribute to his opposite number.
"We knew it would be an emotional night and that would add to the start that Hull produced and they did just that," he said.
"John's like all the blokes in Super League, a good bloke who works hard, and as coaches we all have sympathy and empathy with everyone's situation. We wish him all the best and we wish Hull all the best for the rest of the season."
