However, the Greece international, speaking at the club's Lennoxtown training complex where Celtic this morning announced they would make a £10,000 donation to the Haiti Disaster Appeal, refused to be alarmed at a possible double-figure gap opening up.
"I have no problem with that," he said.
"That's football. You can lose and draw games and at the moment we are nine points behind.
"But we don't care about what Rangers are going to do, we have to look at our team, we have to focus on ourselves.
"We will look at how we improve, how we play better football and, of course, win games.
"We are a big team and we must go and try and turn the situation around because our ambition is to win games and win the title.
"There are a lot of games out there, a lot of points.
"Personally, come the end of the season, I will not be happy if I don't have the trophy in my hands."
Meanwhile, Mowbray remains adamant that he did not tell Scott Brown he wanted to sell him.
The Parkhead club said on its website earlier in the week that it was considering legal action after one report claimed that the Hoops midfielder was informed of the manager's intent to move him on in a meeting before Christmas.
The newspaper stood by its story but the Celtic boss reiterated his stance on the matter.
"The bottom line is I am a guy of integrity and honesty," he said.
"I understand the vagaries of journalism but (if) you push me in to a corner and write something that just didn't happen - sometimes you have to make a stand. Fact.
"I don't like it when I see things printed that never happened.
"I think it's right that we take a stand against that.
"The daft thing about is it that there are so many grey areas.
"Do I talk to my players? Every day. It's my job is to talk to footballers.
"Was there a meeting at Christmas time telling him (Brown) he could go? Never.
"He didn't misunderstand me.
"It was a total mis-truth and I think the club and myself have made that pretty clear.
"It's not disruptive because it's not true."
The former Hibernian and West Brom boss would not deny that he is set to move for Danish international Morten Rasmussen.
He said: "I don't want to sit and discuss any players because you move from one to the next to the next.
"So let's move and we will wait and see."
Mowbray revealed further his exasperation with the Scottish media when he batted back one suggestion that striker Scott McDonald is a target for Wigan.
"I am interested in Lionel Messi, I am interested in Ronaldo if we can get him away from Madrid," he retorted sarcastically.
"I don't think there is a story there.
"It's just typical (of the media), I would suggest, but there you go."
Responding to reports linking him with Parkhead, Rasmussen told Danish television station TV2: "A move to Celtic would obviously be interesting for me.
"As long as nothing is certain, it's difficult for me to say much.
"It's a big club and it has always been a dream of mine to play outside Denmark but we will have to wait and see what happens."
Meanwhile, Celtic are set to snap up Motherwell youngster Paul Slane.
The 18-year old is out of contract at the end of this season and Fir Park interim manager Craig Brown told STV: "I believe a deal is almost done.
"We've not seen much of the boy play because he's been injured and then ill recently. But we offered him a fresh deal at Motherwell which he has turned down."
Scottish Premier Winner 2009/10 Win Outright: Celtic 2/1