A 3-1 opening day loss at home to Aston Villa resulted in Gunners supporters questioning Wenger's status as manager, expressing their unhappiness at the club's lack of progress in the transfer market.
Arsenal responded with a 3-0 victory in the Champions League qualifying first leg at Fenerbahce and then secured a first Premier League win of the season at Craven Cottage.
"For us it's very important that we can get a win here after playing at Fenerbahce," said Wenger, who reported no update in Arsenal's transfer activity.
"We had two good games, at Fenerbahce and, where we played the way we want to play. We were in control.
"You never know how you respond to a game like that (in Istanbul), because it was intense. Maybe the positive result meant the mental side counter-balanced the fatigue.
"We knew the last 20 minutes would be difficult. When they got to 3-1 I was a bit worried, but they didn't put us under pressure."
Wenger was happy for Podolski, who has been linked with a move away from London as Wenger bids to reshape his squad before the September 2 closure of the transfer window.
The Arsenal boss, who said the Germany forward is an important member of his squad, added: "I'm pleased for him, because he did not always start recently, more for balance of the team than for personal performance.
"He has always a high spirit, he's a very important player in the team and he can score goals.
"Everybody loves him in the squad, I want to keep him."