Gloucester secured their first victory away from Kingsholm in any competition since February 26 as they outscored their hosts by three tries to two.
Freddie Burns scored a try in a personal haul of 14 points while Akapusi Qera and Olly Morgan also crossed over for a breakthrough away success.
But Redpath was in no mood to celebrate his team's victory following the devastating motorway pile-up near Taunton, said to be among the worst UK collisions in memory.
At least seven people have been killed and 51 injured while Police have said the death toll was expected to rise as the recovery operation continued.
"For me it is a very humbling experience when you have to travel and see what happened 40 minutes up the road on the M5," Redpath said.
"We are in a privilege position playing sport and sometimes you get bogged down about records - winning away from home or losing home records - they are really irrelevant.
"It is about putting your heart and soul in to your team, your game and trying to live your life in the right way.
"Some people sitting out there have a lot more to worry about than us winning or losing."
Gloucester went in to the break 14-11 in front after tries from Fijian international flanker Qera as well as Burns.
Exeter replied through New Zealand Maori representative Hoani Tui, who scored their only try of the half, with fly-half Gareth Steenson adding two penalties.
Gloucester added a third try at the start of the second half through Morgan before Burns exchanged penalties with Chiefs replacement fly-half Ignacio Mieres.
A subdued Exeter performance earned some reward in the final moments, when Matt Jess crossed to at least secure a losing bonus point, but Gloucester were well worth their win.
Redpath added: "I was delighted with our attack and defence and when we were in the right areas of the pitch we looked to score so that was crucial.
"Defensively we were really strong and if we've controlled some higher field position we would have scored more.
"Exeter are a strong scrum-and-drive, confrontational side so it was important that we did defend. I thought from one to 15, and also the subs that came on, we put in a big shift defensively.
"To win away from home is great. There is plenty to work on - but we don't need to be giving away soft three-pointers and we gave away six points in the first half which we didn't need to give away so those are the little things that we have to brush-up on.
"It was disappointing to give away a late try. We were going for the bonus-point try, we weren't winding down the clock, because we were going to play and win."
Chiefs head coach Rob Baxter said he was disappointed with the defeat, especially at home, but he was thankful that they came away with the losing bonus point.
"To come away in the end (with a losing bonus point) was mightily pleasing and at least we got something for our endeavours," he said.
"The way that the last five of the game was going, when it looked increasingly like that game was slipping away, it was good to take the opportunity of that losing bonus point.
"Physically, again, we committed a lot to the game but the reality is that there were 23 or 24 turnovers.
"That is a real tough lesson for us. We paid the price for some sloppy stuff and came away with just the one point. We missed some regulation tackles and not really made them work for their tries.
"They soaked us up defensively and they managed to control the game.
"As the game wore on and they had a lead it was relatively difficult for us to look at the game in any other way.
"We talk at length about making sure that we are in the fight and we get something from as many games as possible. We got another point today - it is not the end of the world.
"It brings it home that you have to work really hard every week because, as I told the players, being at home doesn't guarantee you a win but you have the opportunity to bring your crowd in to the equation."
Defeat for Exeter was further soured by Fijian centre Sireli Naqelevuki suffering a fracture to his lower right forearm late on which will rule him for several weeks.
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