"We tried to play from too deep and when points were scored against us we gave the ball back too cheaply," said Back.
"We kicked in areas where there was no competition and gave them a free kick back.
"The passion, desire, work-rate and effort is fantastic and belies the position we are in but we have to combine it with some smart decision-making.
"We definitely have the players that are able to do it and we need to do it under pressure. We have to learn quickly. There are still a lot of points to be won.
"We know that from last season when we were in a similar position. We got what was needed to consolidate our place in the Premiership last season and we believe we can still do that this time."
Ryan Davis claimed all Exeter's points with five penalties to three from Leeds' Ceiron Thomas as Chiefs handled the pressure of being favourites instead of underdogs.
"As I said to the players in the dressing room, this was our biggest win, without doubt," said Baxter.
"The pressure that is on a team when you are expected to win, or when things are going well, is totally different."
Promoted Exeter led 6-3 at half-time but Baxter still felt a change of tactics was needed.
"Although we started with a controlled display and got some penalties we were going through the motions a little bit.
"We re-grouped at half-time, having given away a lot of possession and ball in the first half.
"We had players making offloads who would normally carry. We almost tried to play pretty and I think you have to beat Leeds by being direct, physical and hard. We got back to that in the second half and ultimately that is what won us the game.
"We are a team that thrives on tempo and that was lacking at times in this game but for us to come through the second half as strong as we did was great credit to the players."
Exeter face another home game against struggling Sale Sharks next and Baxter added: "You start to feel an improvement when you see back to back wins together.
"We've jumped up the table because we've beaten Saracens and now Leeds."
On a bitterly cold afternoon at Sandy Park, Davis, in his first season with the Chiefs, landed five penalties from six attempts to take the Devon side up to sixth place in the table.
Leeds, seeking their first Premiership win of the season, went into the game without key forwards Steve Thompson and Hendre Fourie, both on England duty against Samoa at Twickenham.
The two sides have met on two previous occasions at Sandy Park in the old National Division One with the Yorkshiremen having won on both occasions.
Fly-half Davis put the Chiefs ahead with two penalties in the opening 10 minutes.
The home side dominated the early passages and it was not until midway through the half that the visitors mounted their first serious attack.
From a 15-metre ruck in front of the posts, Leeds worked the ball to the blindside and centre Henry Fa'afili was stopped close to the line.
Chiefs won the ball at the turnover and cleared their line before Leeds were penalised at their lineout to ease the pressure further on the Exeter line.
Their next attack also faltered when centre Scott Barrow gave a grubber kick to the left corner but it was too long for wing Peter Wackett as Andrew Higgins patiently waited for the ball to go over the line for a 22-metre drop- out.
Leeds captain Marco Wentzel tried his speed down the left but his chip ahead was too hard and then fly-half Thomas saw his 35- metre penalty attempt hit the left upright.
With two minutes of the half remaining, Chiefs were penalised for a late tackle and Thomas found the gap between the posts to leave them trailing 6-3 at the break.
Leeds should have scored the first try 10 minutes after the restart but the hosts defended stoutly only for the visitors to level with a simple penalty from Thomas.
Davis's penalty restored the lead and two more successful kicks left the visitors needing to score twice to win the game.
With two minutes remaining, Thomas slotted a long-range penalty to give Leeds a much-needed losing bonus point.
Exeter Chiefs: Arscott, Higgins, Dollman, Rennie, Foster, Davis, Thomas, Sturgess, Alcott, Budgen, Hayes, Hanks, Johnson, Scaysbrook, Baxter. Replacements: Shoemark for Rennie (51), Whitehead for Alcott (70), Tui for Budgen (57), Slade for Baxter (63). Unused: Moon, Gannon, Cowley, Mieres.
Leeds Carnegie: Stephenson, Blackett, Fa'afili, S. Barrow, Wackett, Thomas, Mathie, Hardy, Nilsen, Gomez, T. Denton, Wentzel, Myall, Oakley, Browne. Replacements: MacKay for S Barrow (61), Fury for Mathie (70), Swainston for Gomez (55), To'oala for Oakley (70), Paul for Browne (61). Unused: Parkes, Alonso, Hinton.
Referee: D Pearson (RFU).