Draghi on Tuesday opened the door to tweaks in the bank's aggressive stimulus policy, fuelling market expectations the bank will announce a reduction of stimulus as soon as September.
Utilities, whose constant dividends flows become less attractive when monetary policy tightens, fell 2.4 percent, suffering their biggest one day loss since November.
Shares in Spanish power network operator Red Electrica , Italian gas firm Italgas and German heavyweight utility E.ON were among the top losers in Europe with losses of more than 3 percent.
Their losses helped drag the pan-European STOXX 600 index down 0.8 percent.
However shares in banks, which have long suffered from the ECB's ultra loose policy, were boosted by Draghi's remarks with the euro zone sectoral index ending up 1.4 percent.
"Today Draghi moved his first step towards indicating that ECB monetary policy will become less accommodative in 2018," said UniCredit chief euro zone economist Marco Valli.
"Unless an unexpected shock materialises, a formal tapering announcement is likely to come at the ECB monetary policy meeting scheduled on 7 September," he added.
Shares in banks such as Caixa, Deutsche Bank, Sabadell and Bankia - which are more sensitive than others to the rate cycle - were among the top five euro zone bank gainers, all up over 2.4 percent.
Bankia got an extra boost as investors cheered to its deal to buy smaller peer BMN in a $924 million deal.
A weak spot among banks was Italy's Carige which fell 3.4 percent to a fresh record low on mounting talk the troubled Genoa-based lender will need more capital than the 450 million euro initially planned to repair its finances.
Autos fell 1.5 percent after German auto parts supplier Schaeffler slashed its profit guidance on growing price pressures and high costs. Schaeffler shares tumbled 12.8 percent.
"Schaeffler flagging increased pricing pressure will almost definitely raise concerns across the supplier space," Jefferies said in a note. "Schaeffler's profit warning will reignite the debate on the resilience on supplier margins and organic growth (post pricing) as we approach the 'peak' of the cycle."
German drugmaker Stada dropped 3 percent after Bain Capital and Cinven failed to win the required shareholder acceptances to take over the firm.
Stada, which have rallied nearly 26 percent this year, however came off earlier lows after Reuters reported that the private equity groups were discussing a new offer.
A.P. Moller-Maersk the world's biggest advertising agency WPP fell 0.5 and 0.8 percent respectively after falling victim of a global cyber attack.
Gains among mining firms Anglo American, ArcelorMittal and Rio Tinto helped prop up the basic resources sector.
(Editing by Jeremy Gaunt)
By Danilo Masoni and Kit Rees
