After solid early pressure from Chelsea was rewarded with a ninth-minute opener from Fernando Torres at the Turk Telekom Arena on Wednesday, Gala controlled the game for long spells.
Mancini reshuffled his pack to tactically stifle the Londoners and the hosts gained their reward through Aurelien Chedjou's equaliser just after the hour.
The 1-1 draw means that the tie is still finely balanced heading into the return at Stamford Bridge on March 18, with an away goal giving the Premier League side a slight edge.
But Mancini felt that his side could have been heading to London in a more comfortable position.
Asked by Sky Sports whether he was disappointed to be coming away on level terms, the Italian said: "Yes, because (in the) second half we probably deserved to score another goal.
"(We gained) a lot of confidence from the second half, but we had too much respect for Chelsea.
"Maybe we were too deep (in the first half), we played with fear but I'm happy.
"One-one is a good result, we have another game."
Striker Didier Drogba, an idol at Chelsea following his eight-year spell at Stamford Bridge, insisted that Gala had proved how dangerous they could be with their second-half performance.
"Chelsea is a better team on paper but tonight we showed we could create some problems," he said.
"I want to go there (Stamford Bridge) and make a good result and qualify. I know the atmosphere at Stamford Bridge but it's possible.
"We were a bit naive at times but we have time to work and solve these problems.
"If we score a goal there, it's a different game - 1-1 is not a bad result for us."
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