The Blues were held to a 1-1 draw in their opening pre-season friendly in Dublin after Michy Batshuayi’s opener was cancelled out by trialist Eric Molloy’s late goal.
Chelsea begin the new Premier League season away at Manchester United on August 11, and Lampard admits there is work to do before the trip to Old Trafford.
Lampard said: “Fitness was our issue, we’ve been working hard on it, even this morning.
“Fitness was always going to be an issue against a team that’s halfway through their season. We certainly pushed ourselves to the limit.
“The quicker we get there the better. It’s about individuals getting fit. Some of the young lads were really good.
“We want to get a level of fitness and intensity in their game.”