Does Salvation By Faith Exclude Regeneration?

There are many texts that say that one believes unto salvation. Those Calvinists who put regeneration before faith are forced into affirming (as a logical result) that the salvation that comes from faith, repentance, and conversion is not regeneration. He is regenerated without faith but saved by faith. Once this false proposition is accepted, every text that speaks of salvation resulting from faith is then interpreted in light of that presupposition, and thus the salvation that results from faith is viewed as not including regeneration. 

But, if one honestly looks at all the texts that speak of salvation that comes by faith he will see that it is not possible to exclude regeneration from that saving. We cannot do it in Ephesians 2: 8 for instance. "For by grace are you saved through faith and that not of yourselves." We have no right to say that Paul excludes regeneration from this saving. In fact, the context shows that it includes it. And, if it is included, then regeneration is by grace through faith. 

"The gospel is the power of God unto salvation to everyone who believes it." (Rom. 1: 16) Why would we exclude regeneration from this salvation?