The midfielder opened the scoring with a twice taken spot-kick as the Reds went on to win 6-3 courtesy of other goals from David Ngog (2), Maxi Rodriguez (2) and Dirk Kuyt.
The Assistant boss - who took charge of first team affairs in the absence of Kenny Dalglish - was delighted for the No.26 and revealed that he was more than satisfied with the squad's second outing of pre-season.
Clarke told Liverpoolfc.tv: "He did well. He had the added pressure that he had to take the penalty a second time. He showed great composure. He also enjoyed some nice touches and some good forward passes. We all know there is a lot more to come from all of the players and Charlie Adam is one of those that will improve throughout the pre-season."
He added: "We've got to be happy with the fact we scored six goals. We are disappointed that we conceded three - although one of them looked at least three yards offside.
"It was a good work-out. We got the fitness work done and that is what you are trying to do at this stage. We have a lot of things we need to improve but we can take a lot of positives too."