I want to downgrade from iOS 7.1 to iOS 6 on iPhone 4 but I have problems. Read Description?

I have an iPhone 4 that I updated to iOS 7.1 from iOS 6 but the iPhone has become laggy and slow. Now I want to downgrade it to iOS 6. All the methods on downgrading require iTunes 11.0.5 or older such as iTunes 10.7 but when I connect it to these versions of iTunes it gives an error that "iPhone requires iTunes 11.1 or later. Go to apple and download the iTunes" so I can't use these methods. Can anyone tell how to downgrade using the iTunes 11.1 or later (newer)? Or how to make the iPhone 4 work with iTunes 11.0.5 or older so that I can use the old methods that are present on google? What should I do?

First, did you save your SHSH blobs for iOS 6? If you didn't, then you're out of luck. Without them, there's absolutely no way to ever go back.

I did a video on this about a year ago @
It's a bit confusing, I'll admit, but I think you'll get the general idea.

There's reason the phone should be slow if it's got a *good* install of 7.1

I have seen problems where the upgrade has not worked properly. Try doing a full reflash before scrapping 7.1, it costs nothing but a bit of time.

Back it up to itunes - the latest or any version new enough to work with 7.1

Disconnect and press both home & power for around 30 seconds - do not release them until you get to the "Connect to itunes" image.

Then connect it and do a restore. (Apple's confusing terminology, it's actually a full reflash of the operating system).

After that completes and it starts up as a new phone, select restore from itunes and put your backup on it.

If it's still no good, the same "Force restore" method may work with an earlier version of itunes? Never tried it, my iphones (4, 5, 6) all work fine on the latest OSs the take.