A late penalty left the team with a deficit to make up next week at White Hart Lane in the round of 32 second leg against FC Dnipro.
Matheus was felled by Jan Vertonghen, with Yevhen Konoplyanka succeeding from the spot to secure a home win after a fairly even and open contest at the Dnipro Arena.
A minute of silence in respect of those killed during the troubles in Kiev was held before kick-off, with many in attendance singing the national anthem.
The pitch at the Arena was in bad condition after the winter period - very firm and with numerous bald patches on the pretty uneven surface. It was certainly not going to be conducive to an exhibition of easy on the eye football.
The team lined up with Etienne Capoue as the deepest of the midfielders, with Nabil Bentaleb and Paulinho ahead of him, while Andros Townsend and Nacer Chadli were pushed on in support of Roberto Soldado.
Both teams were struggling to adapt to the surface in the early stages with the only alarm coming when Rusian Rotan broke away and played wide to Konoplyanka, but the player who reportedly attracted interest from English clubs in January had his low cross intercepted and the danger was averted.
At the other end, a devilish cross from Chadli was met at the near post by Soldado and goalkeeper Denys Boyko somehow reacted quickly enough to block.
Rotan attempted to catch Friedel out after the goalkeeper cleared his lines but his effort on the return lacked height and the American was able to gather. On 24 minutes Friedel was called on to make a much bigger save when Matheus was clean through on goal and, with perhaps almost too much time to think, stroked goalwards only to be denied by the leg of the keeper.
Moments later Friedel was again in action to deny Roman Zozulya. The team had the authority and possession in the game but Dnipro looked dangerous on the counter-attack.
Paulinho was fouled when put through by a superb ball from Soldado, with the referee pointing to the edge of the area when the offence appeared to be inside. Townsend flashed the free-kick just wide.
Soldado came very close to dispossessing the keeper Boyko when he dithered before making a clearance, the Spaniard putting in a challenge but the ball did not run kindly for the striker.
Dnipro began the second half in a lively fashion without really troubling Friedel. Zozulya was booked for diving after the goalkeeper chased a loose ball following a dipping free-kick into the area, but then Soldado should have scored at the other end after Paulinho squared across goal.
A change was made on 63 minutes, with Christian Eriksen taking over from Townsend. Almost immediately Eriksen had the ball in the net but a flag curtailed any celebrations.
The Konoplyanka looked set to score after a mazy run and only a last-ditch block from Michael Dawson prevented him picking his spot. Friedel was then alert to a Matheus piledriver from 20 yards.
Eriksen was making a difference, pinging the ball around with real quality and Soldado was unfortunate not to score with a volley from one of his teasing crosses.
On 79 minutes Matheus burst through into the area before going to ground under a challenge from Vertonghen. The referee pointed to the spot and Konoplyanka struck off the post and into the net.
Kane came close from Eriksen's corner and Roman Zuzulya then struck the inside of the post with a header from Rotan's corner.
It was advantage to the home side coached by Juande Ramos - it should make for quite a night at the Lane next week.