The All Whites face El Tri in the second leg of their 2014 FIFA World Cup playoff and will need to overturn a 5-1 drubbing to play in the finals in Brazil.
McGlinchey said New Zealand's players believe they are better than the Mexicans made them look in the first leg and this was proving to be a source of frustration for the squad.
A fierce determination to prove they are a decent football team is uppermost in the players' minds as they prepare for the return at a sold-out Westpac Stadium.
"We feel we are a lot better than what we showed in Mexico City and we are determined to come out of this tie with our heads held high," McGlinchey said.
"We are a talented squad and we are going to have real go on Wednesday night.
"We will try to put them on the back foot and press them a bit higher than we did at the Azteca.
"We need to get on the ball more and if we do all these things we feel we can get a positive result.
"Obviously Mexico are a tough team and the conditions were against us.
"Yet we should not use that as an excuse because we should have done a lot better and played more football.
"You can't play a game and have only 20 per cent possession.
"It is going to be extremely difficult but we'd like our fans to know that we are going to give it everything we've got."
McGlinchey said he thought the All Whites may have treated the Mexicans with far too much respect, defending too early and too deep.
"They were under a lot of pressure themselves but I don't think we capitalised on that," he said.
New Zealand's poor performance in the first leg drew some disparaging remarks from Mexican legend Hugo Sanchez, who is now a television pundit.
The former Real Madrid star described the All Whites as 'a bunch of buddies who play football only because they are not good enough to play rugby".
Sanchez's remarks have not gone down too well in the New Zealand camp.
Some have said that this might just provide the demoralised team with the extra motivation it needs.
McGlinchey took a more rational view of the matter.
"I heard about it, yes, the boys have been talking about it," he said.
"But I don't think we need any more motivation than trying to reverse a 5-1 defeat.
"No one was happy with that and we certainly have a point to prove to a lot of people."
As if the 5-1 drubbing was not enough of a shock to McGlinchey's system, the sudden resignation of his club coach Graham Arnold means that life at the Mariners will not be the same when he returns to Australia on Thursday.
"I heard about it in Mexico through the media and it did come as a bit of a shock," McGlinchey said.
"Arnie has always been open enough to say that he wanted to go abroad.
"He's been brilliant for us and I am sure that everyone at the club would wish him all the best."
McGlinchey said he could not speak highly enough of the legacy Arnold will leave at the Gosford club.
"Arnie has to take all the credit for what we have achieved as a club in the last three years, to be honest," he said. "He came in and turned the club around.
"We reached two grand finals and for a small club like ours this was absolutely fantastic.
"Arnie is a great man manager and he gave me a role that suits me and I have played my best football in Australia in the last three years.
"He is the best manager I have worked under and he made me a better and stronger player.
"So it is going to be difficult to adjust to not having him there because he has been a mentor to a lot of us.
"We will just have to adapt but I'm sure Phil Moss will do a good job.
"It's his first gig but he has been Arnie's assistant for a long time and he knows the ropes."