Midfielder Rosicky struck in both halves of Arsenal's 2-1 win in what was only his second league start of the campaign. Arsenal's sixth win in the last seven league games moved them - at least temporarily - above Chelsea into fourth spot and they are only a point behind Tottenham, with both their main rivals in action on Sunday.
Wenger said: "Tomas was fantastic. He is an important player for us. Unfortunately he was out injured for a long time. But every year he gives us a push at the end of the season. I hope he finishes his career with us. I rate him that highly."
Wenger has challenged his side to maintain their winning streak and is convinced they will win the battle for a Champions League spot.
He said: "I am very pleased, it is three big points. We have 22 points out of the last 27 but we know our target is to continue to do that until the end of the season. We know we have one target to win our games, then we don't have to look at Tottenham or Chelsea. If we lose our games, then you have to look at the results of the others.
"Our attitude is simple, we have to win the games. Can we finish fourth? I believe we will do it. We are conscious as well we have to give 100 per cent commitment in every game and it will be difficult and edgy to the end. We are ready for the fight and we always tell the players 'don't look at everyone else, just focus on ourselves'."
Wenger confirmed Jack Wilshere and Theo Walcott will be available after injury for next weekend's clash with Norwich. The Arsenal boss also had no complaints with the second-half red card shown to defender Per Mertesacker for a professional foul on Shane Long inside the box.
Albion could only manage a reply from the resultant spot-kick by James Morrison but manager Steve Clarke was happy with his side's performance.
He said: "I thought we played well. They scored in the first half with one of the very few chances they created. We had good control in the first half but didn't really create enough. We could have had a penalty for a challenge on Claudio Yacob on the edge of the box (by Laurent Koscielny). On another day that was a penalty and would have changed the complexion of the afternoon.
"We were disappointed to lose the second goal at the start of the second half. It was crucial for us to get back in it and we gave away another soft goal, a bad goal to lose. At 2-0 it is difficult to chase the game. We made a couple of changes. Then the penalty and the red card does change the game and gives us the chance to get something from the game."
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