Simon King's side struggled to string together a consistent run of results last year - finishing ninth in the Principality Premiership and exiting the SWALEC Cup after a semi-final defeat to Neath.
But Carter, who has scored 140 tries for Aberavon in 228 appearances, argues they are a much better side than last year's showing suggests.
"I've been here 10 years and we've been expecting things every year," he said.
"I think we've got to have silverware here for the club and for the supporters. That's got to be our target.
"We've had a good pre-season, everything has been a lot sharper this year. The boys have been lifting a lot of weights and giving it everything so hopefully we can push on up the league a bit more."
In his time at the Talbot Athletic Ground, Carter has become the first player to score 100 Premiership tries, bringing up the milestone against Bridgend in the final match of last season.
Ninety two of those have come for the Wizards with two for Neath and six for Carmarthen Quins earlier in his career.
"It's been 10 years now since I started, I've played with some good players in that time and the tries have kept coming along nicely," Carter said modestly.
"There are some good new young players coming through all the time. We've got a few in the back row who are looking good in pre-season.
"We just need to be a bit more accurate in our plays, a bit sharper and a bit more aggressive. I think we've done that over the summer and maybe we can now look to push on towards the top three."
Carter's try-scoring prowess would be ideally suited to next weekend's Foster's National Sevens at Cardiff Arms Park.
Sadly for the Wizards, Carter is unavailable but he thinks Aberavon could cause a few shocks.
"A Premiership Sevens tournament has been on the cards for a few years now and we've got quite a few sharp youngsters," he said.
"Steff Andrews and Jon Phillips at full back have plenty of pace so I think we'll do alright.
"As long as we play well as a team then the tries will come."
Tickets for the Foster's National Sevens are on sale now at just £10 for adults, £5 for Under 16s and £20 for a family ticket (2 adults, 2 children). Go to wru.co.uk/nationalsevens to purchase tickets or call 0844 8471881 (Ticketmaster) or 02920 230130 (Ticketline). Personal callers can also purchase tickets from the WRU shop, 8 Westgate Street or from Ticketline, 47 Westgate Street.