A goalless draw with Leyton Orient on Monday made it four consecutive stalemates since Dutton took charge.
He now has seven draws and six defeats in his opening 13 games as that first win still eludes him.
In the last two games, against Harrogate and Orient, Walsall have set up to attack and looked more likely to score as Dutton insists on entertaining supporters in the final weeks of the season.
When asked if draws could be enough to survive, Dutton said: “Potentially they could be.
“We have seven fixtures left and if you offered me seven points now, I think that would get us safe.
“But, it’s a very poor mentality to try and set up to draw games and get over the line in that manner.
“We want to win games and attack and entertain. That’s what we’ll be trying to do.
“Time is Southend and Grimsby’s enemy for sure, but we don’t want to look at them and limp over the line.
“We want to pull away and we have the quality and personality to do that. We just need to get the monkey off our back, get that win and then move on.”