The Upton Park academy graduate assisted both of James Collins' goals in the draw, as the Hammers were denied a win by Robin van Persie's 91st-minute equaliser.
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"It was nice to get involved and get the minutes under my belt. It's been a long time since I've played properly.
"Like I said, three or four games and I'll be back to my best. It it was a great start on a personal note, but it still feels like a missed opportunity."
The former Liverpool man highlighted the Red Devils' greater quality as being crucial in their comeback, but backed his new team-mates to go and grab a good result in the replay at Old Trafford.
"They're a quality side and have done that countless times," Cole continued.
"When you've got world-class players like Van Persie and Giggs, they can combine like that. I thought we defended really well, good concentration, good heart, good discipline and we were unlucky not to win, but it's a good start.
"Of course it does [feel like a missed opportunity]. You've got to go to Old Trafford, but we've done it before so we'll have another go."