Newcastle created the better chances and were awarded a first half spot-kick, but Gordon’s poor effort against his former side was saved by England teammate Jordan Pickford.
It was a third clean sheet in 32 away Premier League games and Howe chose to focus on that positive.
"I have to credit the players because it is a difficult environment to play in and it is a much better defensive display from us too. Big steps forward," Howe told the BBC.
"We stood up to the physical test and were technically very good. We are trying to break barriers and have an outstanding season. I think we are capable of more and we have some tough fixtures to come.
"Anthony handled the occasion very well. I think his all-round game was very good. He will be disappointed with the penalty. But credit to Jordan Pickford for the save."
With the international break next, Howe is hoping to have forwards Alexander Isak and Callum Wilson back by the time they host Brighton & Hove Albion in a fortnight.
"We hope so. They are two huge players for us. When you take any focal point out of a team it has an impact."
Everton manager Sean Dyche hailed his side’s resilience, especially as they continue to have several defenders on the sidelines and had midfielder James Garner fill in at right-back for this game.
"We have been patching together teams which has been a hard task," he said. "I'm pleased for the back five, I thought they were very good. All things considered, we take the point, a positive point, and we have looked strong in the last three games."
Everton had a penalty shout of their own when Dominic Calvert-Lewin appeared to be impeded by Dan Burn.
"(Calvert-Lewin) is trying to finish it. Let's put it this way, if that's in the middle of the pitch is he giving a foul? I would say absolutely," Dyche said.
