Martinez's side have just six points from their opening seven games following the 2-1 loss to Manchester United at Old Trafford on Sunday.
A two-week interval now awaits, with Martinez hoping his players bounce back when their season resumes at home to Aston Villa in just under a fortnight.
He told BT Sport: "We want more points. We are not hiding from the fact. We feel we have dropped many points.
"But we have played four of the top six teams already. We are getting sharper and stronger.
"We need to get a good break now and after we'll try to get the results our performances deserve."
Defeat to Louis van Gaal's men came amid a stunning performance from David de Gea, who made a string of fine saves late on and kept out Leighton Baines' first-half penalty.
De Gea's efforts ensured Radamel Falcao's first goal since joining United on loan from Monaco was decisive, which came after Steven Naismith had cancelled out Angel di Maria's strike.
Martinez added: "I just felt that De Gea made two world-class saves that stopped us getting a positive result.
"The second-half performance deserved more than we got."
An injury to John Stones added to Martinez's woes, with the Everton boss confirming the defender has an ankle problem.
The Spaniard revealed: "He has a problem with his ankle, ligament problems. It is a massive blow as he plays with incredible arrogance."
‘After Manchester City’s recent form, maybe they’re the underdogs against Manchester United!’ Former Red Devils defender on this weekend’s derby
‘Arteta, Alonso, Emery, me… none of us were physical players – we needed the understanding of the game. That probably helped us move into management’: Premier League boss reveals reasons for natural career progression
