While the club suffered the loss of midfielder Marouane Fellaini to Manchester United ahead of the deadline, they were able to keep full-back Leighton Baines despite interest from Old Trafford.
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"When the window closed there was a different environment around the football club," he told reporters. "We feel it is a fresh start.
"For us, there is a feeling that the season starts now, we have done many good things in the previous games but now we need to pick up points and get our season started."
Everton have drawn all three of their Premier League fixtures so far this season, with Ross Barkley one of the standout performers.
The 19-year-old has featured heavily under Martinez and made his England debut on Friday against Moldova and Martinez has now tipped the midfielder to continue his impressive form domestically.
"We all saw what he is capable of doing in the future," Martinez continued.
"He has incredible potential and we need to keep working on that potential so he has a terrific career ahead of him."