Daniel Nardiello put the home side ahead before Rickie Lambert hit a brace to snatch Saints victory.
Adkins said: "It was an excellent three points as Exeter gave us a very tough game. We knew it would be a tough game, especially after the weekend's events.
"We have come away from home, it was a difficult pitch to say the least, and you could see that with their goal as the ball didn't bounce. We knew that was going to be an issue, but great credit to the players because they have ground out a win.
"We played with two out-and-out wingers and created good opportunities ourselves, but that exposed us in the middle of the park. We changed that second half as the game has gone on and they were two great goals from Rickie Lambert.
"It was a good three points for the players and all credit to Exeter, but it was a massive three points towards taking us to where we want to go."
Source: PA
Source: PA