Training & Nutrition - Training to increase stamina

I've been training hard all year and have made a lot of progess. I'm usually well off the front in the group that I normally ride with and decided to do a long ride yesterday with a group I knew was much faster and stronger. I did fine for the first 30 miles, kept up and hung on over hill and dale but the first scheduled stop was 35 miles in. I finally had to sit up, even though I knew that once I was out of the 20-27 mph paceline I would go much slower even if I worked as hard.

My legs were fine, I wasn't out of breath, my heart rate was below LT but all of these other parts of my body were screaming out for a rest--lower back, feet, butt. After stopping for just two minutes I was fine again. All the pains went away

Other than just continuing to train hard and challenge myself by riding with people who are stronger and faster than I am, is there some specific training routine I could be doing to increase my ability to maintain a high level of output for a longer amount of time?

It seems to me that what I need is to increase my stamina. Are there any specific techniques to do that?

I have had similar experiences while running and swimming (for both I have trained for racing and long distance). For me, it is a signal that I need to add sprints to my workouts . . . or incresase the length of my sprints if I am already doing them. . . where you push hard for two minutes, rest 30 seconds, etc. I find these are better on workouts alone and I add these every other day. I am new to biking, but I imagine the theory is the same. Nutrition, fuel, strength training, stretching and sleep are also important. Lots of interesting research is out there with endurance sports.

Sandy