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That result still leaves The Lions six points from safety but the manager is optimistic that his side can turn the corner and pull themselves away from the danger zone.
"People won't believe me," said Tuttle after the game. "But I still think we can get out of trouble.
"My team put on a real performance after our last two disappointing games against QPR and Sheffield Wednesday.
"We need to turn this result into three points, starting this weekend. We have to start getting results and in my heart I know we can get them."
In a tight, scrappy game, The Lions were left to rue missing a hatful of early chances when Paul Robinson was harshly sent off for a "foul" on Hull City's Craig Fagan - the club's 13th of the season. Referee Lee Probert consulted with his linesman, who gave the decision the visitors way despite the fact the defender seemingly won the ball, and dismissed the laid-out centre half.
"I thought it was harsh," continued Tuttle. "The way the ball went I thought Paul Robinson won it.
"Andy Marshall gave him concussion when he came flying in. He didn't even know he had been red-carded."
Hull, however, were unable to make their extra-man advantage tell as the home side took the initiative in the second half. But despite all their possession, Millwall once again lacked the imagination to unlock The Tigers' defence. And when a Jody Morris pass went astray, they were made to pay as Jon Parkin ran through the defence to score with little over ten minutes left.
A superlative strike by captain Dave Livermore saved The Lions' blushes, but had the manager brought on winger Marvin Williams five minutes earlier, the game may well have been won.