Sanchez was recalled to the starting XI after shaking off a hamstring problem, but was taken off midway through the second half following a strong challenge from Matthew Upson before the break.
Ramsey lasted just nine second-half minutes after he was brought off the bench, having suffered what seems to be a recurrence of his hamstring injury.
"It looks like [a hamstring] but I don't know yet how bad it is," Wenger explained in reference to the Welsh midfielder.
"Visually it doesn't look good when the guy stops straight away and sits down - that's not good news.
"I left him out today because I wanted to be cautious with him and I had to bring him on because we lacked a little bit of offensive power but it was not the best of decisions.
"You can't say it's not a worry because after a while he does not play with a free mind. He's not overplayed, since he's had these problems I've been a bit more cautious with him.
"Sanchez had a knock to his knee, I don't think he was himself after he got his knock he was never really comfortable and I don't know for how long he'll be out or whether he'll be out.
"It was a heavy tackle. I was ready at half-time to [bring him off] but he said: 'No, it's okay I can go on'.
"But when I watched him play I thought 'no'. He became worse and in the second half I didn't see him."
Sanchez later tweeted that "sometimes the love for the game and anxiety to be on a football pitch works against you", perhaps indicating that he should have listened to Wenger's half-time concerns.
Arsenal looked in complete command of the game in the first half, but lost some of their fluency after going in 2-0 up at the break and were made to sweat when Andrej Kramaric scored his first Leicester goal just after the hour.
But Wenger's men held on to move into the top four, with the Frenchman relieved to bounce back after Saturday's derby defeat at Tottenham.
"In the first half we were in control but they had one or two good chances on the counter-attack," he added.
"Second half we lost our cohesion, our technical superiority, and Leicester were always dangerous going forward.
"At 2-1 it became a bit nervous but what was important for us today was to get the three points."
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