Most Hoops' fans have given up on the title race but Mowbray is adamant that, although expectations are fading, there is not any less pressure on his players.
"If anything, there was more pressure on the team to get a result because, again, not all of you, but the way some of the Scottish media work, they like piling it on," he said.
"So we have to keep going and keep winning matches, that's what we do.
"There is no lack of motivation. There is no greater motivation than every time you pull on a Hoops' shirt.
"You should be 100% focused on trying to win because the supporters of the club come to support our team home and away and they deserve a performance.
"I thought they got a very professional performance."
Warming to the issue of the Scottish media, Mowbray played down the significance of Aiden McGeady's claim that Dougie McDonald had not been "impartial" during last week's Old Firm derby at Ibrox.
Before Maurice Edu scored a last-gasp winner for the home side, Hoops' captain Scott Brown was controversially sent off after tangling with Rangers' Kyle Lafferty, who escaped unpunished.
Before the game an unknown source at Celtic had let it be known that the Parkhead club were not happy with decisions they believed had gone against them this season, including in the first two games against Rangers.
McGeady's remarks could see the Celtic midfielder hauled up before the Scottish Football Association but Mowbray moved to defuse the situation.
"I haven't seen that article," he said.
"If a journalist used the word "impartial" I'm pretty sure he (Aiden) didn't know what it meant.
"I am wary talking about it. I can see the headline 'Mowbray says McGeady is ignorant' and I am not saying that.
"If it was a clever journalist speaking about impartiality, he might not have got the context of the question, I don't know.
"But I would be surprised if Aiden came out and criticised the officials or their impartiality, I'm pretty sure he wouldn't."
Keane showed why the Parkhead club are reportedly paying him £65,000 per week during his loan spell from Tottenham with two fine finishes.
However, Mowbray has given no thought to the possibility of making the deal permanent at the end of the season.
"That's what he does," added the former West Brom boss. "That's why he is here, to stick the chances away when they come along and he did that today.
"Extending his deal is not something that has crossed my mind. We will wait and see.
"I don't know what Robbie's thoughts are with regards his football career.
"He is still a young guy, he is contracted to Tottenham and I don't know what he thinks about his future.
"But he is here until the end of the season and hopefully he has a few more days like today where he makes a difference."
Bairns boss Steven Pressley was "devastated" for his players who remain three points adrift at the bottom of the table.
"I am devastated for them," he said. "Absolutely devastated for them.
"They are disappointed because they know that winning is the most important aspect but in terms of what you can ask for from players, I can't ask for any more than that.
"Robbie Keane was the difference between the teams on the day, he produced two wonderful finishes and we missed a number of opportunities.
"But our football at times was scintillating, we did all the things that were asked of us.
"So I honestly couldn't ask for any more from the players.
"We have 10 games to go now and out focus is beating St Johnstone this weekend."
Source: Team Talk