"It's disappointing to lose a football match, but I have just said to the players, they have done us proud," Clark said after the game against his hometown club.
"We took Newcastle to the wire, we were a threat all evening and contributed to what was a very, very good cup tie played with high intensity at high pace, and quality play from both sides at times.
"My two strikers certainly caused Newcastle problems. I thought they were the two outstanding players for us.
"Having said that, the rest of the team made a real contribution. Jordan Rhodes and Theo Robinson have different attributes and they gave the defenders some real problems.
"I think it will be difficult to find a better cup tie in the country this week."