Josip Ilicic had given Fiorentina a 17th-minute first leg lead at the Stadio Artemi Franchi before Seydou Keita headed home an equaliser 13 minutes from time.
The midfielder's leveller could yet prove a crucial away goal, although Garcia was left disappointed not to be heading into next week's second leg in front.
"We deserved to win today. We had lots of chances to win the match," said the Frenchman.
"We were up against it in the first 20 minutes, but then we turned a corner and stopped giving it away in midfield.
"We were ambitious and got a goal, which is always important when you're playing away in a European knock-out tie.
"We shouldn't just play to get through on away goals in the second leg - we have to try and win the game.
"In the last 70 minutes tonight it was the same Roma side I saw against Juve [in Serie A last Monday] and Feyenoord [in the Europa League last 32].
"We showed character and personality. We built the play well and showed we could stretch them [Fiorentina].
"It was a good performance from us this evening and I think we could have got the victory."
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