The Chiefs went third with the win, though they may be overtaken by London Irish if the Exiles can overcome second-placed Saracens.
Baxter said: "I think that the lowest we can go after the weekend's round of matches has been completed is fourth but we have a good chance of staying third at Christmas, which is fantastic.
"It is a bit of a reward for the hard work that the guys have put in. We are a competitive side; we have been competitive in every game and we have taken something from nearly every game.
"It is probably that which means we are quite high up the table. It is not that we are stringing together win after win but we are there or thereabouts each week and that makes a big difference."
Exeter went into the break 9-6 ahead after three penalties from their Argentina fly-half Ignacio Mieres to two from his opposite number Joe Carlisle, who saw his third attempt on the stroke of half time slip under the bar.
Mieres increased the Chiefs' advantage with two more penalties before being replaced for the final quarter by Gareth Steenson but former England fly-half Andy Goode kicked a penalty three minutes from time for Warriors for a losing bonus point
"It was a really good, solid, Premiership win obviously dictated by kicks at goal," said Baxter. "Worcester created one scoring chance when they fumbled the ball on the touchline and we created all the other try-scoring opportunities.
"I am a little disappointed that we didn't convert in the first period when we were all but over the line and a little frustrated that we didn't convert at least one other opportunity that would have opened up the game.
"We showed good composure and we put a lot of pressure on Worcester for the majority of the game. We played very good territory and defensively we looked very sound."
The Warriors lost Matt Kvesic after just 14 minutes as the flanker was stretchered off with an injury to his left ankle before being taken to hospital for an X-ray.
It left head coach Richard Hill searching to sign a couple of back row players as Kvesic will be sidelined for at least a couple of weeks, leaving him with just Jake Abbott and Sam Betty while the rest are in the treatment room.
The Warriors boss said: "Initially it didn't look good. We thought it was a break and dislocation by the way everyone reacted around the player before he was carried off on a stretcher.
"But he wasn't too bad when he came off. He didn't have any gas or air and there wasn't a splint on the injury. We now think that he may have broken a small bone just above the ankle.
"We are three props down and now four back rows down so we have to call on the same players to go to Bucharest next Sunday. In the backs we have plenty of options."
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