Captain Michael Vaughan says England must work on their bowling and batting ahead of their remaining Super 8 games.
Vaughan took the wicket of the in-form Niall O'Brien
"We're not playing the full game but it's very rare that you play at 100%.
"At the moment we're playing around 80% and I'd like to see us play a bit more than that," he commented, following Friday's 48-run win over Ireland.
They had Ireland 139-6 at one stage but allowed them to reach 218 and Vaughan said: "We need to try and bowl teams out when we have an opportunity."
He continued: "It would have been nice to nail it when they were six down but they played well and we didn't get it quite right for a few overs," said Vaughan.
England now travel to Antigua, where they face Group B winners Sri Lanka on Wednesday and favourites Australia four days later.
They also have concerns over the performance of the top order batting, including Vaughan himself, although he insisted there was no crisis.
Vaughan made six, Ed Joyce fell for one, while Ian Bell hit a painstaking 31 from 76 deliveries against the Irish.
He said: "We will have to work hard over the next few days to make sure the top order fires against Sri Lanka on Wednesday, but definitely the most important thing was to get two points.
"We're not firing consistently, but Ed Joyce has just got two fifties and Ian Bell is hitting the ball OK.
"My form is pretty patchy. It started well but in the last two innings I haven't got any runs. I'll have to work hard over the next few days with the coach and make sure I get a bit of confidence and rhythm."
Paul Collingwood provided the batting impetus for England
Vaughan also took a turn with the ball against Ireland, sending down nine overs of off-spin and taking 1-34, and he expects to do more bowling as the tournament progresses.
"I just tossed a few up and they came out OK," said Vaughan. "I've been working on my bowling in the nets and I'll hopefully bowl a few more times in this tournament."
Meanwhile, man of the match Paul Collingwood, who scored 90 and took 1-38, said England had surpassed their pre-match target of 250 by scoring 266.
But only some big hitting in the last 10 overs from Collingwood, who hit three sixes, Paul Nixon (19 from 15 balls) and Ravi Bopara (10 from five) made England safe.
"It takes a bit of time to get in on these wickets and later on in the innings you can make up the run-rate," said the Durham all-rounder.
"We were looking for a total of about 250, so 266 was a good total on this pitch.
"It nibbled around a little bit with the new ball and the Irish bowlers put us under pressure. But the pitch got better as the day went on and those last 10 overs helped us."