The Serie A outfit started well against their Premier League opponents and took the lead through Erik Lamela after 21 minutes, but a Frank Lampard equaliser and a last-minute Romelu Lukaku effort saw Jose Mourinho's men come out on top.
Garcia felt that there were plenty of positives to take from the performance, though, with new signing Kevin Strootman looking lively in a creative midfield role.
However, the Roma boss admitted that his side still had plenty of work to do in order to build up their fitness ahead of the start of the new Serie A season.
"We had a good first half, keeping possession and creating a few good scoring opportunities," Garcia told the media following the defeat.
"In the second half, partly due to the number of changes in the sides, we were unable to play the same way. Chelsea made many substitutions and their players were more physically fresh.
"The only problem I saw in our second-half performance was fatigue. We were tired and therefore couldn’t keep the ball the same way as in the first half."
The Giallorossi kick off their league campaign with a trip to Livorno on August 25.