"The rally we're seeing here is a bit of a head fake," said Christian Magoon, CEO of Amplify Investments. "I think there's a bit of relief that he was deadlocked and she had a solid performance."
"It looks like Hillary Clinton earned the market's vote today," said James Abate, chief investment officer at Centre Funds. He added "there is a basic assumption that Hillary Clinton is going to be good for the status quo."
Investors also kept an eye on oil prices, as U.S. crude futures fell 2.74 percent to settle at $44.67 per barrel as hopes for an output-limiting deal during an oil producer meeting in Algeria faded. On Monday, WTI rose more than 3 percent.
"As we've seen so often in the past, the possibility of a deal has been talked up a lot in the weeks leading up to tomorrow's meeting and now it seems the opposite is happening," said Craig Erlam, senior market analyst at Oanda, in a note.
U.S. futures rose sharply overnight, with Dow futures having risen more than 100 points shortly after the presidential debate concluded. But by Tuesday morning, however, futures had pared most gains and dipped into negative territory. The Mexican peso also rose sharply overnight against the dollar and was last trading 2.4 percent higher versus the greenback.
"The jury is still out on who won last night," said Adam Sarhan, CEO at Sarhan Capital. He said that, even though a number of experts said Clinton won, there were a number of polls showing Trump won. "I don't think last night hit the nail in the head for either candidate."
"The election in November is one of the biggest risk events facing the markets this year and the way markets responded to the first debate makes it clear which outcome is more favourable. Clinton appeared to edge the first debate which has provided a lift for investors, albeit only a slight one as the polls remain extremely close and the campaign has a long way to go," said Oanda's Erlam.
The second of three debates between Trump and Clinton will be held October 9.
"The Presidential Election will now recede into the background until the next debate on October 9. If one candidate definitively pushes his or her nose in front of the other in the polls, then the market may exhibit little reaction to the race for the White House prior to November 8," said Jeremy Klein, chief market strategist at FBN Securities.
Stocks closed sharply lower on Monday ahead of the debate, despite strong gains in oil prices.
"The market is desperately looking for two things: clarity and a bullish catalyst. Until we get one of those, I expect this sloppy trading to continue," said Sarhan.
Also on market watchers' radars was Deutsche Bank, which saw its shares hit a fresh all-time low on Tuesday, weighing on European equities. The pan-European Stoxx 600 index traded lower for most of the European session before closing 0.06 percent higher.
Deustche Bank shares in past 6 months