A delighted Reid said: "People expect us to be at the bottom of the table but we never look down and we have a belief in what we are trying to do at the club. We think we can play in the right manner and we are progressing as a club.
"To come here and win is pleasing for us and I think over the 90 minutes we just deserved it.
"When Gary McDonald equalised it looked as though there was only going to be one winner and that was Aberdeen but we seemed to get a new lease of life and began to look more threatening."
The Accies boss was particularly pleased to see Australian midfielder Wesolowski score his first goal for the New Douglas Park side.
He said: "That was James' first senior goal, which is incredible because in training he is a great finisher but for some reason he has not managed to get on the scoresheet. I hope it is the first of many."
The Hamilton manager refused to criticise Lee Miller for a late challenge on his goalkeeper Tomas Cerny, who had to be withdrawn at half-time following the tackle.
"The ball was there to be won," he added. "He has hit the goalkeeper but I would expect my centre-forward to go in and try to win the ball. I have no problem with that."
Aberdeen manager Mark McGhee admitted his side did not deserve to take anything from the game after a lacklustre performance.
"I think we were out-fought and out-worked, particularly the younger, creative element of the team," he said.
"We didn't really fire or create enough today and we didn't keep the ball well enough. We were literally out-fought by a determined Hamilton team who went the distance. I can have no complaints as we didn't play well."
McGhee thought his side would go on and win after midfielder Gary McDonald equalised with 15 minutes to go.
He said: "If I was playing today I would have wanted us to go on and win after we got it back to 1-1 but there has to be an element of the team that are more cautious.
"One of the things we have said in the dressing room is that when you get it back to 1-1 you have to maintain a certain element of caution, while the other element of the team go on to try to win the game.
"Once we got back to 1-1 we shouldn't have lost the game."
But McGhee claimed his side's inconsistency was not down to a lack of belief.
He added: "It isn't to do with confidence. The younger players in the team still have to understand that football is not just about skill and taking people on.
"There is another side to the game which Hamilton demonstrated well today and that is determination, which can get you very far."