The English struggled throughout the match but somehow managed to hold the Italians and take the match to a penalty shootout, which they lost 4-2 in Kiev.
It had not been a smooth ride for Roy Hodgson's men who luckily topped Group D after beating Sweden, Ukraine and a draw against France.
"At times, the football hasn't been fantastic, we haven't blown people away. We stuck together. We fought hard. We gave every inch of effort we can give. At times, we have found it difficult to keep the ball," Gerrard said on Monday.
Italy had 65 percent of possession in the quarter-final with a pass completion rate of 81 percent compared with England's 61.
"The possession stats speak for themselves. It tells you that moving forward as a nation, we do need to try and improve with the ball," the England captain said.
According to England manager Roy Hodgson, lack of ball possession was due to tiredness as players were left chasing shadows.
"If you are saying 'Could we have kept the ball better at times and could we have made more use of the good situations we got into?' I would have to agree with that. The players realize that too. That is an area of the game where we need to keep working and improving," Hodgson said before the team flew home.
Hodgson, however, said the team is moving in the right direction before World Cup 2014 qualifying begins against Moldova in September.
Players like Andy Carroll, Danny Welbeck Jordan Henderson and Alex Oxlade-Chamberlain gained valuable experience in a major tournament.
"There is good reason for optimism. We have some players coming through ... we have to see the positives where we can and try and ignore the fact that, yes, it is another failure on paper because we have not got past the quarterfinal stage.
I don't believe there is as much negativity as perhaps there was. But the only way we can build upon what we have done here is by qualifying for Brazil and, when that tournament comes around, trying to better our previous record," Hodgson said.