The Swans went 1-0 down but an incredible comeback led by a Sam Clucas brace and Jordan Ayew's tap in after Petr Cech's mistake lifted the Welsh club off the bottom of the Premier League table and out of the relegation zone.
As quoted by Wales Online in his post-match press conference, Carvalhal said: "I understand the market is very hard for us and we are doing the best we can to achieve good players.
"I hope this victory will help with their decisions, because so far most don’t want to come to Swansea. It is not because of good offers, or we are not trying, but the reality some do not want to come, some clubs are waiting on other players, so we must wait. We understand that.
Swansea have not made any signings this month despite being bottom for the whole of it but this is largely because players have been hesitant to join the precariously positioned club. Carvalhal only wants the highest quality too.
"I want players to cover gaps, to do specific things we do not have. It does not mean I think we are weak, it means if we have them we can jump to another level. If we do not achieve this, I trust these players," he said.
"They are going to new levels with confidence high. It is a consequence of the dynamic and the way they are working very hard. We are still waiting and let’s see if something happens.
Carvalhal was evidently impressed with the result and used another beautiful analogy - something the Portuguese manager is becoming renowned for - to describe his club's chances of staying up
"We are very happy. To win against Arsenal after beating Liverpool means I'm proud of my players. They deserve all the credit. We created more chances than them. I told the players we are ready to do something different and I said after the win at Watford we are not dead, we are breathing.
"We have a chance of staying up. We are not in intensive care, but we are not far away from the doctor saying we can go home.”