The newly-promoted Foxes marked their Premier League return in dramatic fashion as Chris Wood struck an 86th-minute equaliser to deny Martinez's side victory.
"It is a bit of a mixed feeling because we knew it was going to be a difficult fixture against a team with promotion and a good feel about them," he told BBC Sport.
"We were a little bit soft in the way we conceded the first goal and then when we got the second goal we were a little relaxed and it was a bit too easy.
"Overall, disappointed that I feel we threw two points away. I'm sure that for Leicester it will feel like a victory and for us a defeat, but it is a start."
Leonardo Ulloa hit City's first goal of the afternoon to mark his debut for the club following his £8m switch from Brighton & Hove Albion.