It's almost never acceptable to put two wires underneath one screw on a receptacle, but, tying them together first and using a pigtail to do it is fine IF you use the right wire. Many receptacles have holes in the back that can take up to two wires and are clamped by the screw. WIth those, it is acceptable to use both the screw and the holes which would give you three or as many as six connections. I will stay that it is important that the wire gauge be identical when using two wires in the back...the clamping plate on at least some does not swivel, and getting it tight to two diverse sizes may not happen!
Now, if you still have the old receptacle available, take a look and see if the tab between the two hots was broken. IF it was, then you have NOT wired it properly. A red wire is typically the identifier of a switched power lead, and it may have been used to switch one half of the receptacle for something like a table lamp. By tying all of the leads together, that switch no longer can function, and, if the power happened to be on the other leg, bad things would happen when the switch was turned on.