Arsene Wenger has told Arsenal fans that Olivier Giroud is staying at the club this season.
"We kept going and the spirit of the team was absolutely outstanding", Wenger said.
Substitute Ramsey smashed in an angled drive - from a corner which was won after Mesut Ozil handled in the build-up - before Giroud showed athleticism and strength to meet Granit Xhaka's corner.
That held until Arsenal took advantage of a lapse of discipline from Leicester right before halftime.
The Frenchman is expected to play second fiddle to club-record signing Alexandre Lacazette this season, meanwhile, following the striker's big-money move to London earlier this summer.
"I'm happy the goals we conceded we can work on together".
Arsene Wenger also added after the game that he was delighted that the 30-year-old had made a decision to stay at the Emirates, after he had offered him the opportunity to leave.
Craig Shakespeare's Leicester side caused all sorts of problems for Arsenal's back three over the course of the game and went ahead for the first time in the game when Jamie Vardy put the Foxes 2-1 up in the 29th minute. "We were quite good last year on corners and with a bit of work we can get that out of our system", added Wenger, who has been given another two years in charge of Arsenal.
"Obviously I knew that I was going to have a chance so we tried to push".
Cech initially tipped over Riyad Mahrez's shot but the latter turned provider from the resulting corner. In the following minutes, the hosts tried to tighten their defence and get back on their front foot, keeping Leicester's goalkeeper Kasper Schmeichel on his toes. "We see players like Hector Bellerin, Alex Iwobi coming through, Reiss Nelson and Joe Willock have had a fantastic pre-season".