Woods: I want to put town right
The Mariners were deservedly beaten 2-0 by Blue Square Conference South side Bath City at Blundell Park in the first round of the competition.
And it means Town have still to win since the former striker took over from Mike Newell three games ago, with Saturday's reverse the poorest performance so far.
But Woods remains hopeful he will be given time to turn things around.
He said: "Whether it affects my chances (of getting the job) or whether I want it is irrelevant at the moment.
"The bigger picture is about the football club and (against Accrington Stanley) we finished on a high – although the performance wasn't great – and this has been a step back.
"Being part of a result like this, being the nature that I am, makes me want to put it right.
"I wouldn't do anything unless I didn't think I could do it properly, and that is what I have done all of my life.
"I may not always achieve what I set out to, but I have always given absolutely everything I can to try and get there. If I didn't think that I was capable of doing it, I wouldn't put my hat in.
"There needs to be a system in place where everybody knows who is in charge, who is doing what, and ultimately we have to get some players that can do what we want them to do.
"It needs the right decision. There have been too many changes over the last few years on the playing staff and in management. The next decision is the big one, the key one.
"It needs someone to come in for three or four years and build the football side of the club."
Goals from Chris Holland and Darren Edwards were enough to inflict Woods' second defeat.
Afterwards, he pulled no punches, admitting some of his players had simply not been good enough.
He said: "Credit to Bath, I think they deserved to win the game, and that is massively disappointing.
"You have to be confident, you have to use the abilities you have got, you have to be prepared to get things wrong at times, and we didn't.
"We had a good chance early on with the header (by Barry Conlon) but in general play, although we had a lot of possession, we didn't create anything.
"There is too many of them (not taking responsibility). I picked the team so I'm not ducking out of responsibility either.
"Once they cross the white line you expect people to stand up, use the ability that I believe they have got, but they didn't do that on Saturday.
"I think it is down to lack of ability at times in certain areas. We weren't good enough.
"It is the quality that we need, whether they are young, whether they are old. People are picking a team because they add something to it or to use their attributes, and if you don't use the attributes you have been picked for, then common sense says you are not going to get picked again.
"It came as a big disappointment to me. We trained on Friday for 45 minutes and that is as bright as I have seen them since I took over.
"So we left on a high thinking if they are that bright and take it into the game, then you have to be massive favourites.
"I can still join in the five-a-side games but what I can't do is go and play out there, because you have to run, you have to take responsibility and you have to be right for the games.
"For whatever reasons, individually we weren't good enough."
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