It would have been a perfect finish for Morrison, who had taken over from out-of-form Walter Pandiani. He may be able to slot away the goals for the Republic of
Ireland but in the blue shirt of Birmingham he has struggled to make an impact this year.
Bruce said afterwards: "Unfortunately Clinton, who seemingly scores every match for Ireland, missed the easiest chance of his three recent goal opportunities.
"But I'm delighted with a point as I believe Tottenham have the makings of a very good side."
As a result of the Morrison miss Birmingham had to be content with a home draw against an equally shot-shy Tottenham side that last won away from home on Boxing Day.
Jermaine Pennant started for City but it proved to be a difficult occasion for the youngster on his return following his month in jail for motoring offences.
Bruce added: "He wanted to play and he appreciates the support he had from the fans. Jermaine wanted to get his first appearance out of the way and now he just wants to get on with rebuilding his career and life."
Pennant lacked his usual sparkle but this was hardly surprising in view of his incarceration and he eventually made way for Julian Gray in the 55th minute.
It proved to be a crucial period in the game as in the 58th minute Spurs broke the stalemate when substitute Stephen Kelly fired home a low cross-shot following a defence-splitting pass from Michael Carrick.
Birmingham salvaged their point with a 65th minute equaliser from Darren Carter but they were sadly off the pace for much of the match.
Spurs often looked the sharper but they lacked a cutting edge as they failed to take advantage of some skilful approach work by the stocky Andy Reid.
The former Nottingham Forest player turned out to be the most dangerous player with two efforts which went just wide.
Birmingham's most anxious moment occurred when a Fredi Kanoute cross was mis-hit by Jermaine Defoe and Jamie Clapham got himself into a tangle clearing off the line.
City, on the other hand, were sadly out of touch in the first half when Pandiani had a nightmare 45 minutes and was completely out of touch.
Emile Heskey battled bravely and was involved in a tussle with Ledley King in which the Spurs skipper usually came out on top.
Later Birmingham were indebted to Maik Taylor. The Northern Ireland international goalkeeper made two superb reflex saves to keep out a Mido header and a shot from Kanoute.
Tottenham boss, Martin Jol, said: "We badly needed a win but I can live with a draw as we had problems with our substitutes."
MAN OF THE MATCH: Maik Taylor (Birmingham City) - Made two brilliant saves in a couple of minutes in the second half that kept City in the game. He was outstanding in midweek for Northern Ireland in Poland and maintained that form to ensure Steve Bruce's misfiring side secured a hard-fought point.