The Czech scored what proved to be the winning goal at the Emirates Stadium on Boxing Day in what was his first Premier League start of the season.
Rosicky had suffered with thigh problems earlier this month, but was handed a surprise start against Harry Redknapp's side, ensuring Arsenal took maximum points despite Olivier Giroud's dismissal for an altercation with Nedum Onuoha.
And the 34-year-old feels his smart finish can bolster hopes of appearing more regularly in the new year.
"It was my first start of the season so I wanted to show the boss that he can use me more," he told reporters.
"It was an important victory for us because we played for a long time with 10 men, but we dug deep and won the game.
"This is a very important part of the season so we are glad with the win."
Arsenal have now gone four games unbeaten in all competitions, but sit 15 points off Premier League leaders Chelsea.
Rosicky was cagey when asked about the prospect of being involved in the title mix-up.
"You can see that it will be very tough and we will see how everyone is doing after the Christmas period," he added.
‘He instantly popped into our ratings as one of the best U21 midfielders in Europe. The impressive thing is Slot has made him into more of a no.6' Inside Ryan Gravenberch's transformation at Liverpool
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
