"We could never imagine a Chelsea side winning a trophy without those quality players, and always knew replicating the success of the great players would be hard. I want to stretch them because that's what pre-season is all about", the 41-year-old told Chelsea's website.
"Our level and performances were not good enough and the reason they were not happy with us and negative".
Unlike the English Premier League, the Irish league ends in October, meaning that Bohemians are now in the middle of their domestic season.
Since Roman Abramovich took over the London club they have become characterised for the rate at which they burn through managers.
Pedro, 31, has played for some of the best managers in his illustrious career and now has a chance to work under Lampard during his swansong.
"We turned it around and won the Europa League but you can see that this season all of the fans are very happy we have the gaffer back at the Bridge". Now we have something unusual - the transfer ban - which gives a chance for a lot of young players, players coming back from loan.
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New Chelsea manager Frank Lampard said he was pleased with the team's response to his "taxing" pre-season program following a 1-1 draw at Irish side Bohemians in his first match in charge.
"At that moment no one could imagine a Chelsea side winning a trophy without players of their quality and we have to try to keep the level and replicate the success all the players in the past have had. We have to take responsibility and know that there are a lot of things [going on] around us, but we have to work hard to get better".
Lampard was missing a few of his key players who were still yet to report back from their holidays, and so fielded quite an inexperienced side.
And, when asked questions about Lampard's experience, he declared: "The whole experience he has as a player, playing at the highest level, under a lot of very good managers, his personality, behaviour and experience - there is nothing to be anxious about as a manager". I've never had such a hard start.
Lampard returned to Stamford Bridge earlier this month, replacing Maurizio Sarri as Chelsea manager, having spent 13 years at the club as a player, becoming the Blues' all-time leading scorer with 211 strikes.