"We are all striving for the same goal," he told Celtic's official website.
"We want to try to win some trophies and be successful in 2010, just like everybody does.
"We hope to find the consistency of performance that gives us the results to bring the SPL title back to Celtic Park.
"We also want to do well in the Scottish Cup and generate a feelgood factor around the club."
Mowbray experienced plenty of Old Firm derbies as a player but only one as a manager, October's 2-1 defeat at Ibrox.
"The derbies are always exceptional occasions with great atmospheres," he said.
"There is expectation and anticipation, but hopefully the team has a great confidence from the way we've been playing.
"We've been creating a lot of chances in recent weeks and we can also take positives from the first derby."
Celtic lost that encounter at a time when victory would have put them seven points clear of a Rangers side struggling for form.
Mowbray added: "For long spells we were the team driving forward and we'll take belief and confidence from that."