Redpath had demanded a huge improvement from his side following last weekend's 42-6 reverse at Harlequins, but he did not look set to get it as they were forced to soak up wave after wave of Bath attack during the opening half an hour.
Two Sam Vesty penalties during that period gave the visitors a 6-0 lead, but Gloucester's scrum dominance and punishing driving line-out took its toll with hooker Darren Dawidiuk and wing Charlie Sharples claiming tries and fly-half Tim Taylor kicking 11 points.
Redpath said: "I thought our pack were outstanding. There were some great performances across the board from the pack and that set a platform for the game.
"(Operations manager) John Brain has done a lot of good work with our scrum and that was important for us. We put a big emphasis on that part of the game and it was really important we got that right today, and we knew we could have a go at them there.
"(Forwards coach) Carl (Hogg) also did a lot of work on our driving as we conceded three tries from drives last weekend.
"Today was about that detail that we practised and having the right collective emotion attached to it. Today we played as a team, defended as a team and got our rewards as a team."
Redpath was also full of praise for his side's determination in defence during that tough opening, believing coming through it without conceding a try was key to victory.
"We never got any field position in that first 25-30 minutes, Bath retained possession well, but we gained a lot of confidence from defending multi-phases," he said.
"We turned them over in certain phases but couldn't get out of our own half and it allowed them a chance to attack.
"But we grew in confidence after defending for long periods.
"Ideally you don't want to get into a situation like that, but after last week's performance it was really important that we dig in today and showed lots of character and passion."
And Redpath also revealed how a "brutal" review of the defeat at Quins had teed the side up for derby week.
He said: "Monday was pretty hard, we had a long review session and you can't not be open and brutally honest when that happens.
"We conceded too many points at Quins away and we had to put that to bed on Monday or we would have dragged our feet through the disappointment of that game.
"From Tuesday onwards it was about understanding how tough Bath was going to be, they had won two, narrowly lost one, and were confident in what they had achieved over the last three or four weeks.
"We needed to be back to where we should be, not necessarily where we were against Quins."
Bath boss Sir Ian McGeechan agreed that the opening 30 minutes had been critical, with his side's inability to take their chances proving costly.
He said: "For 32 minutes we were pretty good. We kept Gloucester in their own half with no rugby to play and controlled it.
"With a little bit more execution we probably could have been a couple more scores up.
"They defended well so you have to give them credit, but a couple of poor executions and we gave them a lifeline."
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.