Giroud had scored 12 Premier League goals in just 11 starts last season, but Lacazette was selected for Arsenal's opener and netted inside two minutes.
Alexandre Lacazette marked his league debut for Arsenal with a goal on 94 seconds only for Shinji Okazaki to level less than three minutes later.
"I opened the door for him at some stage as I had many strikers and it's important for him to play but I don't want him to go", he said.
Arsenal dramatically scored two late goals thanks to Aaron Ramsey and Olivier Giroud as the club got off to a great start.
In the league's first Friday night start, Arsene Wenger's side was trailing 3-2 with seven minutes remaining but Ramsey grabbed the equaliser and Giroud headed in an 85th-minute victor.
The guests needed only 10 minutes to regain their lead after the restart as Vardy headed in Riyad Mahrez's cross to score his side's third goal and complete his brace.
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"You want the Premier League to be the best league in the world and I think it has to produce this kind of game to produce interest and quality. Giroud in his prime is at the top of his game".
I'm not saying he should be Arsenal's number one striker; that wouldn't be enough if Arsenal were trying to win a Premier League or Champions League which a club of this size should be. It's no doubt going to spoil all of us because the rest of the games are going to suck by comparison.
Then, as they usually do, Arsenal got it back by the end and pulled out a win.
"After that, we get the efficiency".
Like many of Leicester's players, Vardy endured a post-title slump last season, scoring only 13 times in the league, and Shakespeare was delighted to see him back among the goals.
However, despite his impressive display during the match, the Ox's efforts seemed to go pretty unnoticed and has been hardly mentioned in match reports or commentary of the match.
"Lacazette is getting stronger in every game and tonight he put in a very convincing performance".