The Gunners were - having positioned themselves among the Premier League front-runners - expected to dip into the January transfer market for attacking reinforcements.
Schalke's Julian Draxler was heavily linked with a switch to Emirates Stadium, but no deals were put in place and Arsenal will continue as they are.
That means France international Giroud will lead the line, supported by the likes of Lukas Podolski and Nicklas Bendtner, and is expected to build on the 14-goal return he has offered so far.
The 27-year-old frontman claims he is ready to embrace that challenge and considers a lack of movement in the winter window to be a show of faith in his ability by boss Arsene Wenger.
Giroud told the Daily Telegraph: "I understand that Arsenal fans want a big name, but I try to stay calm, to take it easy and concentrate on my job, train well and repay the confidence of the boss.
"He always talks to me, trusts me - that's why he didn't buy another striker last summer and in January. I'm still here because the boss is pleased with my game.
"I know I'm not a player on the same level as someone like (Luis) Suarez because he's been amazing this season but I know I can improve. That's why I'm quite confident of my future here. This isn't a time to doubt myself.
"Sometimes a striker won't score for a month or two. It happens to every striker. But you've always got to believe in your quality and remember that people trust you.
"I feel good here and I really want to win something with this club."
Arsenal's season is likely to be shaped by their fixtures in February, with Saturday's clash with Liverpool followed by a home date with Manchester United, another meeting with Liverpool in the FA Cup and the first leg of a date with Bayern Munich in the last-16 of the UEFA Champions League.
On that run, Giroud said: "I am looking forward to it.
"Even though we will miss Aaron (Ramsey) and Theo (Walcott) we have the quality in the squad. If we believe in ourselves and play with solidarity, like we have for most of this season, then that will be the key to our success.
"We are also better defensively this season. Not only that, Mathieu (Flamini) and Mesut (Ozil) have arrived and we have managed to keep hold of our best players, something that hasn't happened for a few years."