Andy Goode's late drop-goal denied Bath a losing bonus point on Friday night, when victory would have taken them into the title play-off zone.
"We didn't have a lot of ball in the first half and that is not the best way to build pressure," McGeechan said.
"We didn't show the intensity of last Sunday (against Montpellier). We were pretty average and we have no excuses.
"Things have to be far better than they were tonight. We have to look hard at ourselves. We did not do ourselves justice."
The result meant former England captain Lewis Moody ended a difficult week in more pain as tepid Bath slipped to defeat without seriously testing a Worcester side that had won just two of eight previous league games this season.
Moody, his trademark all-action style making little headway in a Bath side devoid of ideas, lasted only 49 minutes before injury forced him off.
And to complete a miserable night for Bath, their England lock Dave Attwood was carried off with his neck in a brace following a lengthy stoppage midway through the second period.
Attwood went to hospital as a precaution, but he was expected to be released tonight after medical staff gave him the all-clear.
Moody, meanwhile, finished second-best after attempting to tackle Worcester wing Marcel Garvey just before half-time, departing for treatment to a head wound before making a brief return that he eventually aborted.
Only two days ago, Moody felt obliged to issue a strongly-worded statement hitting back at suggestions he put commercial gain before his rugby during England's dismal World Cup campaign.
Rugby Football Union elite rugby director Rob Andrew reportedly criticised Moody for leading a senior player delegation that disputed the squad's World Cup payments.
Moody was also targeted by one unnamed team-mate for having too much contact with his agent during the tournament, the claims being made in post-World Cup reports leaked to a national newspaper.
Bath skills and defence coach Brad Davis added: "Worcester played the game in the right areas and deserved their win.
"We can't be up one week, and then not the next. If we want to be in the top four in the Premiership, then these are the sort of places we have got to come to and get four points."
Worcester also suffered their share of injuries during a bruising battle, with prop Matt Mullan hurting his shoulder and flanker Neil Best suffering a suspected broken arm.
"We have now only got two fit props, so it was a bit of a costly game for us," Worcester head coach Richard Hill said.
"But to get the win will give everyone a big boost. We asked for our best performance of the season and I think we probably did that.
"We didn't look jittery. We went out with confidence, although we didn't get the rewards until just before half-time with Miles' try.
"We managed to close the game out, which was key. That was a big psychological thing for us - a massive step forward."
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
$29.99
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.