Despite losing the match, the reaction to England's performance was largely positive as they played attacking football and posed a constant threat to the Italian defence.
Lampard shared the positive outlook following the match, but insists that they need to pick up points in their next two matches against Uruguay and Costa Rica respectively.
"I thought we started very bright, played some good attacking football. There were a lot of positives out of the game, the one negative was that we didn't win it," Lampard is quoted as saying by PA.
"Importantly now [we must] look forward, take those good points, try and keep them going and improve on them. We need to win games."
England's next match comes against Uruguay on Thursday, with both sides looking for their first points of the tournament.