Hearts ended a five-match losing streak with a 2-0 win over St Johnstone on Tuesday night to move six points off sixth-placed Hibernian in the Bank Premier League ahead of Sunday's Edinburgh derby.
Tenth-placed Hearts also face Aberdeen and Ross County before the split and Sutton knows they need to hit top form.
Sutton told Hearts TV: "It was an important win, and I think it was very important performance as well, we have been on a bad run.
"That's what we are capable of doing - we didn't play as well as we possibly could this season.
"We have really got to keep up those performance levels for the rest of the season too.
"I think the trouble is that we've been probably given ourselves too much to do. You never know, we are reliant on the other people.
"I think if we are going to be focused in the next three league games, see where that takes us - hopefully that will be the top six.
"The shame is that we never really put a performance in like that all this year.
"We got two goals, and the way we played - we dominated the game - we could have had a few more. Obviously, it is a great to get a clean sheet for Jamie (MacDonald) and for the boys at the back as well.
"It is tough for us to get in the top six, but we are going to give a good job."
Sutton scored in his second consecutive game but he gave a fair amount of credit to his strike partner Michael Ngoo, who is on loan from Liverpool.
The former Motherwell forward said: "That's a funny thing with goals: as much as I've tapped it in, the thing is that Michael has done the most of the work for me.
"I've been talking to him and the pleasing thing is that we are linking up well. Both of us had lots of shots, lots of chances.
"Even if we are not getting chances for ourselves, or setting each other up, we are certainly helping the team out.
"The signs are encouraging but we have to keep that going."