Saturday's 4-0 result made it four wins from four games for Carrick since taking charge.
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United fullback Shaw said afterwards: "He's brought a lot of changes, but the most important is that he knows this club and knows what it takes to win. He's achieved a lot here as a player and understands the environment perfectly.
"He knows how to bring out the best in each of us, and he really does. Winning makes everyone feel better, our confidence grows, and that's also thanks to the daily demands he makes of us."
Shaw added: "We can't give up now. No celebrations: we need to stay focused, recover quickly and prepare for the next match."
United meet West Ham on Tuesday night.