The month began badly for Everton as they lost at West Brom but a draw against Newcastle was followed by a 3-0 win at Swansea and a 3-1 home victory against Southampton.
Everton are fourth in the Premier League table going into the international break and Moyes is keen to maintain the push for a Champions League berth.
"With the quality of the Premier League it is really hard to qualify for the Champions League but I wouldn't say we can't do it. It is possible and you have to aim for that," he told the club's official website.
"If we fall short and end up in the Europa League then so be it, but in recent years we have been pretty close, finishing sixth, seventh or eighth, so we want to do that at the very least."
Meanwhile, Scotland international Fletcher scored five goals in four matches for Sunderland in September, helping Martin O'Neill's side to go unbeaten throughout the month.
"I'm obviously pleased with the award but results are more important," he told the Sunderland website. "To stay unbeaten in September was a real positive for the lads and I'm pleased I grabbed a few goals as well."
One of the top soccer cleats for control the Nike CTR360 will not let you down on the field in tight spaces.
The adidas Nitrocharge is the most talked about new cleat in years. It was released on May 15 and will take your pitch by storm.
The Juventus jersey for the 2013/14 was released earlier this week. Be the first to wear the colors of the Old Lady.
The new PUMA evoSPEED 1.2 FG. A great new soccer cleat with classic look and first time for PUMA to be on the cleat.
Chelsea won the Europa League on Wednesday. The Blues defeated Benfica 2-1 on injury time goal from Ivanovic.
Borussia Dortmund hears Wembley Calling and are headed to London for the Champions League final.
The Liverpool 2013/14 soccer jersey is available for pre-order. The Reds are eager to compete for silver next season.
adidas has added some color to the Predator line with this new colorway. Released on May 17. Be the first to own a pair.
Bayern Munich are kings of Germany and hope to be crowned kings of Europe at Wembley later this month!
The push for more color on their cleats, adidas has added the infrared colorway to the adiZero f50 Line.