First-half goals from Simon Church, Niall McGinn and Kenny McLean gave the Reds victory as they brought the gap to Celtic down to four points.
Time is beginning to run out for the Dons, with just six more fixtures to make up the points – and with Celtic having a game in hand and a massive goal difference advantage, the Parkhead club are holding all the aces.
But boss McInnes said: "It was important the players showed they were still fighting.
"The pitch helped us as it was in far better condition today, but we had a lot of players playing at the top of their game.
"It was a strong 90-minute performance. In the first half we obviously got the goals but the movement and speed we brought was difficult for Hamilton to contain.
"We've started a lot of games similarly but haven't always managed to get the goals to match, so getting the second was very important to us and the third knocked the stuffing from Hamilton.
"Nobody within our camp feels the season is a write-off. We've still got work to do, and we'll finish where we deserve."
Source: Sky Sports