Rovers dominated for long spells, with Morten Gamst Pedersen and Benni McCarthy both going close on numerous occasions, but there was ultimately no way through for Mark Hughes' side.
The Rovers boss made four changes to the side that held Arsenal to a goalless draw at the Emirates Stadium at the weekend. Matt Derbyshire and Gamst returned to the starting line-up from injury to replace the ineligible Christopher Samba and Bruno Berner, while Tugay returned for the suspended Aaron Mokoena and McCarthy was preferred to Shabani Nonda in attack.
Leverkusen made two changes from their first leg triumph on home soil, with Brazilian defender Juan returning from injury in place of goalscorer Jan-Ingwer Callsen-Bracker, while Paul Freier was preferred to Stefan Kiessling.
With both sides looking for an early goal, the game started at a lively pace, with the ball zipping across the wet surface.
But while the visitors enjoyed much of the early possession, it was Rovers who created the better chances in front of goal. On four minutes, Gamst was brought down 35 yards out from goal and the Norwegian stepped up himself to fire an ambitious free-kick just inches over the bar.
And 10 minutes later, after David Bentley's surging run was cynically brought to a halt by Juan, for which he was duly booked, Gamst again struck a left-foot curler agonisingly over Jorg Butt's goal.
On 25 minutes, Derbyshire was played in on the right-hand edge of the box, Juan again looked to have mistimed his challenge, but Gamst fed the loose ball through to McCarthy, whose shot on the turn deflected marginally wide of the far post.
Just past the half-hour, and in light of Ryan Giggs' controversial goal for Manchester United against Lille in midweek, referee Undiano Mallenco refused to let Bentley take a quick free-kick, but by the time the England Under-21 international was allowed to take a strike, the onrushing defender was less than a yard away.
Rovers' wide men were causing Michael Skibbe's team the most problems and, on 34 minutes, Bentley's outstanding cross from the right had to be headed out for a corner as Derbyshire attacked the ball.
As the half drew to a close, Leverkusen registered their first efforts at goal of the game. Bernd Schneider hit the outside of Brad Friedel's right-hand post with a 25-yard free-kick, before the World Cup star blazed over the bar after breaking into the box.
Fresh from the break, Rovers came out all guns blazing at the start of the second half. Stephen Warnock ought to have done better after breaking free round the back on the left side, but his attempted ball in to a packed box was blocked at the near post.
On 56 minutes, Bentley made another surging run down the right wing before cutting the ball back to David Dunn, whose goalbound header had to be clawed round the post for a corner.
And nine minutes later, Gamst's long throw caused havoc in the Bayer box, but Derbyshire was just unable to turn it home. On 70 minutes, and after some lovely one-touch stuff from the home side, Gamst whipped the ball in, but somehow McCarthy failed to connect in front of goal.
The action looked to be boiling over with 10 minutes remaining when Gamst and Carsten Ramelow squared up, Sergej Barbarez then took a theatrical tumble when confronted by Dunn, before almost all 22 players got involved.
Hughes rang the changes, with Tugay and Zurab Khizanishvili replaced by Jason Roberts and Nonda, and it was the substitute striker who had the best opportunities to win the game.
From a long ball forward, the DR Congo captain got in behind, but his lobbed volley bounced the wrong side of the post, then in time added on, he just couldn't stretch enough to meet Gamst's measured cross.