Roy Hodgson's side remain top of Group H with two home games to go after securing a 0-0 draw against Ukraine.
The result puts England a point clear of Montenegro and Ukraine and three ahead of Poland, who beat San Marino 5-1, but former England international Le Tissier told Sky Sports News that the team's display left much to be desired.
"A 0-0 draw is a good result looking at the result on face value alone - and I'm sure Roy Hodgson would have taken it before the match - but I don't think he'll be particularly pleased with the performance of his team," he said.
"It was really quite scrappy at times; although the defending was good, when we got into the final third of the pitch - even the middle third, really - our passing wasn't good enough and we should have created a few more chances.
"We didn't pick players out well enough and we didn't use the space that we did get on the occasions where we were allowed a little bit. The passing just wasn't good enough.
"I thought Gary Cahill was excellent - he probably just edged out Phil Jagielka, for me, but the two centre-backs were good.
"Early on I thought Karl Walker and Ashley Cole had a few problems against the wide men but they managed to turn it around in the end and contain them pretty well for the most part. You look at all the defensive players that really had the biggest influence on the match.
"I've always been confident that England will qualify and I still am - and this result certainly helps. It puts us in a really good position but there is still work to do."
Hodgson defended England's performance, insisting the goalless draw was a positive outcome, but also admitted that his team had little margin for error after a display that Le Tissier said its fair share of anxious incidents. Read our report here.
"There were a couple of nervy moments; in the first minute the referee took a long, hard look at maybe giving a penalty but Joe Hart didn't touch Roman Zozulya; the referee got that decision right," said Le Tissier.
"There was also a header which Artem Fedetskiy should have done better with - it was a free header only five or six yards out but he completely mistimed it and headed the ball into the ground, and Joe Hart got his hands onto it.
"There was also a free-kick right on the edge of the box which on another day the referee could have awarded as a penalty and you couldn't have argued against it because it was bang on the line. You'd probably have to give the referee a big pat on the back and say 'thanks very much' for giving that one just outside the box."
The result means that England have so far failed to beat any of their main rivals in Group H - their only successes coming against the two teams at the bottom of the table, Moldova and San Marino.
Hodgson's team still have their fate in their own hands and will take on Montenegro at Wembley on October 11 and Poland, again at home, on October 15.
England were held by Poland in Warsaw when Kamil Glik cancelled out Wayne Rooney's goal and it was a similar story against Montenegro away, when Rooney scored again only for Dejan Damjanovic to equalise.
Reflecting on England's results against their chief contenders in the group, Le Tissier said: "It's a little bit of a worry, really. Obviously the draws away from home aren't too bad as long as we do go and pick up the three points in the two home games.
"If we don't go ahead and pick up the six points from the next two games, Hodgson will then be looking at those away games and thinking 'that's where we let ourselves down a little bit'."