Alan Connell fired the hosts into the lead with a 25th-minute stunner before an own goal by Paul Linwood and a spectacular late bicycle kick by Brett Pitman sealed the Cherries' victory.
Linwood scored Grimsby's consolation and Woods has hailed his team's strength of character.
He said: "I thought we showed great character. We could have been adrift at half-time but some questions were asked in the dressing room and the lads responded brilliantly.
"We got a bit of luck for the goal and after that I thought we were the better team for long periods. We could have folded after that first-half display but we came back and I am delighted with the response.
"We still have a lot to work to do in terms of the shape and the organisation of the team but we are improving."